TASK DEFINITION: In this task, you are given a context, a subject, a relation, and many options. Based on the context, from the options select the object entity that has the given relation with the subject. Answer with text (not indexes).
PROBLEM: Context: Latin (Latin: ) is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets., In mathematics, a rational number is any number that can be expressed as the quotient or fraction "p"/"q" of two integers, a numerator "p" and a non-zero denominator "q". Since "q" may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", is usually denoted by a boldface Q (or blackboard bold formula_1, Unicode ); it was thus denoted in 1895 by Giuseppe Peano after "quoziente", Italian for "quotient"., In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization., A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests "prove" that a number is prime, while others like MillerRabin prove that a number is composite. Therefore, the latter might be called "compositeness tests" instead of primality tests., Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers)., A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3., Paul Leyland is a British number theorist who has studied integer factorization and primality testing., Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts. This was a recognizable category of mathematical activity from the 19th century onwards, at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, and so on., In number theory , a Leyland number is a number of the form x ^ y + y ^ x where x and y are integers greater than 1 . They are named after the mathematician Paul Leyland . The first few Leyland numbers are 8 , 17 , 32 , 54 , 57 , 100 , 145 , 177 , 320 , 368 , 512 , 593 , 945 , 1124 ( sequence A076980 in OEIS ) . The requirement that x and y both be greater than 1 is important , since without it every positive integer would be a Leyland number of the form x1 + 1x . Also , because of the commutative property of addition , the condition x  y is usually added to avoid double - covering the set of Leyland numbers ( so we have 1 < y  x ) . The first prime Leyland numbers are 17 , 593 , 32993 , 2097593 , 8589935681 , 59604644783353249 , 523347633027360537213687137 , 43143988327398957279342419750374600193 ( A094133 ) corresponding to 32 +23 , 92 +29 , 152 +215 , 212 +221 , 332 +233 , 245 +524 , 563 +356 , 3215 +1532 . One can also fix the value of y and consider the sequence of x values that gives Leyland primes , for example x2 + 2x is prime for x = 3 , 9 , 15 , 21 , 33 , 2007 , 2127 , 3759 , ... ( A064539 ) . By November 2012 , the largest Leyland number that had been proven to be prime was 51226753 + 67535122 with 25050 digits . From January 2011 to April 2011 , it was the largest prime whose primality was proved by elliptic curve primality proving . In December 2012 , this was improved by proving the primality of the two numbers 311063 + 633110 ( 5596 digits ) and 86562929 + 29298656 ( 30008 digits ) , the latter of which surpassed the previous record . There are many larger known probable primes such as 3147389 + 9314738 , but it is hard to prove primality of large Leyland numbers . Paul Leyland writes on his website : `` More recently still , it was realized that numbers of this form are ideal test cases for general purpose primality proving programs . They have a simple algebraic description but no obvious cyclotomic properties which special purpose algorithms can exploit . '' There is a project called XYYXF to factor composite Leyland numbers ., An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and 2048 are integers, while 9.75, , and  are not., In Algebraic number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in formula_1 (the set of integers). The set of all algebraic integers, , is closed under addition and multiplication and therefore is a commutative subring of the complex numbers. The ring is the integral closure of regular integers formula_1 in complex numbers., Subject: leyland number, Relation: subclass_of, Options: (A) algorithm (B) blackboard (C) branch (D) category (E) complex number (F) decomposition (G) economics (H) engineering (I) integer (J) language (K) latin (L) mathematics (M) meeting (N) natural (O) natural number (P) number (Q) out (R) polynomial (S) problem (T) process (U) rational number (V) ring (W) set (X) test (Y) theorem (Z) theory ([) thought (\) time

SOLUTION: natural number

PROBLEM: Context: Watford is a town and borough in Hertfordshire, England, situated northwest of central London and inside the circumference of the M25 motorway. It is not to be confused with Watford, Northamptonshire which is 55 miles to the north., Chiltern Railways is a British train operating company owned by Arriva UK Trains that has operated the Chiltern Railways franchise since July 1996. It operates commuter/regional rail passenger services from its Central London terminus at London Marylebone along the M40 corridor to destinations in Buckinghamshire, Oxfordshire and Warwickshire, as well as long-distance services to the West Midlands along two routes. Services on the Chiltern Main Line run from London Marylebone to Birmingham Snow Hill, Stratford-upon-Avon and Oxford, with some peak-hour services to Kidderminster., Chesham (, or ) is a market town in the Chiltern Hills, Buckinghamshire, England. It is located 11 miles south-east of the county town of Aylesbury. Chesham is also a civil parish designated a town council within Chiltern district. It is situated in the Chess Valley and surrounded by farmland, as well as being bordered on one side by Amersham and Chesham Bois. The earliest records of Chesham as a settlement are from the second half of the 10th century although there is archaeological evidence of people in this area from around 8000 BC. Henry III granted the town a royal charter for a weekly market in 1257., The Metropolitan line is a London Underground line that runs from Aldgate, in the City of London, to Amersham and Chesham in Buckinghamshire, with branches to Watford in Hertfordshire, and Uxbridge in the London Borough of Hillingdon. Coloured magenta (Pantone 235) on the tube map, the line is in length and serves 34 stations. The section between Aldgate and Baker Street is shared with the Circle and Hammersmith & City lines; that between Rayners Lane and Uxbridge with the Piccadilly line; and that between Harrow-on-the-Hill and Amersham with Chiltern Railways. Just under 67 million passenger journeys were made on the line in 2011/12. The line is one of only two London Underground lines to cross the Greater London boundary, the other being the Central line., Uxbridge is a town in west London, England, and the administrative headquarters of the London Borough of Hillingdon. Fifteen miles (24.1 km) west-northwest of Charing Cross, it is one of the major metropolitan centres identified in the London Plan. Uxbridge historically formed part of the parish of Hillingdon in the county of Middlesex, and was a significant local commercial centre from an early time. As part of the suburban growth of London in the 20th century it expanded and increased in population, becoming a municipal borough in 1955, and has formed part of Greater London since 1965. It is a significant retail and commercial centre, and is the location of Brunel University and the Uxbridge campus of Buckinghamshire New University. The town is close to the boundary with Buckinghamshire, which is locally the River Colne., Pantone Inc. is a corporation headquartered in Carlstadt, New Jersey. The company is best known for its Pantone Matching System (PMS), a proprietary color space used in a variety of industries, primarily printing, though sometimes in the manufacture of colored paint, fabric, and plastics., Northwood Hills is a London Underground station on the Metropolitan line in the area of Northwood , between Northwood and Pinner stations and is in Travelcard Zone 6 ., Buckinghamshire (or ), abbreviated Bucks, is a county in South East England which borders Greater London to the south east, Berkshire to the south, Oxfordshire to the west, Northamptonshire to the north, Bedfordshire to the north east and Hertfordshire to the east., Aldgate was the eastern-most gateway through the London Wall leading from the City of London to Whitechapel and the East End of London. It gives its name to a City ward bounded by White Kennet Street in the north and Crutched Friars in the south, taking in Leadenhall and Fenchurch Streets, which remain principal thoroughfares through the City, each splitting from the short street named Aldgate that connects to Aldgate High Street. The road is situated east north-east of Charing Cross., The London Underground (also known simply as the Underground, or by its nickname the Tube) is a public rapid transit system serving Greater London and some parts of the adjacent counties of Buckinghamshire, Essex and Hertfordshire in the United Kingdom., The London Borough of Hillingdon is the westernmost borough in Greater London, England which had a population of 273,936 according to the 2011 Census. It was formed from the districts of Hayes and Harlington, Ruislip-Northwood, Uxbridge, and Yiewsley and West Drayton in the historic county of Middlesex. Today, Hillingdon is home to Heathrow Airport and Brunel University, and is the second largest of the 32 London boroughs by area., Rapid transit, also known as heavy rail, metro, subway, tube, or underground, is a type of high-capacity public transport generally found in urban areas. Unlike buses or trams, rapid transit systems are electric railways that operate on an exclusive right-of-way, which cannot be accessed by pedestrians or other vehicles of any sort, and which is often grade separated in tunnels or on elevated railways., The City of London is a city and county within London. It constituted most of London from its settlement by the Romans in the 1st century AD to the Middle Ages, but the agglomeration has since grown far beyond the City's borders. The City is now only a tiny part of the metropolis of London, though it remains a notable part of central London. Administratively, it forms one of the 33 local authority districts of Greater London; however, the City of London is not a London borough, a status reserved for the other 32 districts (including London's only other city, the City of Westminster). , Hertfordshire (often abbreviated Herts) is a county in southern England, bordered by Bedfordshire to the north, Cambridgeshire to the north-east, Essex to the east, Buckinghamshire to the west and Greater London to the south. For government statistical purposes, it is placed in the East of England region., Amersham is a market town and civil parish within Chiltern district in Buckinghamshire, England, north west of London, in the Chiltern Hills. It is part of the London commuter belt. Amersham is also from Aylesbury and from High Wycombe., The Piccadilly line is a line of the London Underground, coloured dark blue on the Tube map. It is the fourth busiest line on the Underground network on the basis of the number of passengers transported per year with 210,000,000. It is mainly a deep-level line, running from the north to the west of London via Zone 1, with a number of surface sections, mostly in its westernmost parts. It is named after the road above it between Hyde Park Corner and Piccadilly Circus. Some of its stations are shared with the District line and some are shared with the Metropolitan line. It is the second longest line on the system, after the Central line, and has the second most stations, after the District line. It serves many of London's top tourist attractions including Harrods (Knightsbridge), Hyde Park, Buckingham Palace (within walking distance from Green Park), Piccadilly Circus, Leicester Square and Covent Garden, as well as London Heathrow Airport, the busiest airport in Europe. The line shares tracks with the Metropolitan line between Uxbridge and Rayners Lane, and with the District line between Hanger Lane Junction and Acton Town, then runs parallel with the District line between Acton Town and Barons Court., In cryptography, MAGENTA is a symmetric key block cipher developed by Michael Jacobson Jr. and Klaus Huber for Deutsche Telekom. The name MAGENTA is an acronym for Multifunctional Algorithm for General-purpose Encryption and Network Telecommunication Applications. (The color magenta is also part of the corporate identity of Deutsche Telekom.) The cipher was submitted to the Advanced Encryption Standard process, but did not advance beyond the first round; cryptographic weaknesses were discovered and it was found to be one of the slower ciphers submitted., The Tube map is a schematic transport map of the lines, stations and services of London's public transport systems, the primary system being London Underground, known colloquially as "the Tube", hence the map's name. The first schematic Tube map was designed by Harry Beck in 1931, and it has since been expanded to also include today the Docklands Light Railway, London Overground, TfL Rail, Tramlink and the Emirates Air Line cable car., Subject: northwood hills tube station, Relation: located_in_the_administrative_territorial_entity, Options: (A) amersham (B) baker (C) bedfordshire (D) buckinghamshire (E) cable (F) central (G) chesham (H) chiltern (I) colne (J) cross (K) district (L) east end of london (M) england (N) europe (O) greater london (P) hertfordshire (Q) hyde park (R) london (S) london borough of hillingdon (T) magenta (U) middlesex (V) most (W) new jersey (X) northwood (Y) of (Z) oxford ([) oxfordshire (\) piccadilly (]) river (^) road (_) south (`) south east england (a) street (b) uxbridge (c) watford (d) west (e) west midlands (f) westminster (g) wycombe

SOLUTION: london borough of hillingdon

PROBLEM: Context: Jacquelyn Ellen "Jaclyn" Smith (born October 26, 1945) is an American actress and businesswoman. She is known for her role as Kelly Garrett in the television series "Charlie's Angels" (197681), and was the only original female lead to remain with the series for its complete run. She reprised the role with a cameo appearance in the 2003 film "". Her other films include "Nightkill" (1980) and "Déjà Vu" (1985). Beginning in the 1980s, she began developing and marketing her own brands of clothing and perfume., Papua New Guinea (PNG  Hiri Motu: "Papua Niu Gini"), officially the Independent State of Papua New Guinea, is an Oceanian country that occupies the eastern half of the island of New Guinea and its offshore islands in Melanesia, a region of the southwestern Pacific Ocean north of Australia. Its capital, located along its southeastern coast, is Port Moresby. The western half of New Guinea forms the Indonesian provinces of Papua and West Papua., Shelley Marie Hack (born July 6, 1947) is an American model, actress, producer, and political and media advisor. Hack is best remembered as the face of Revlon's "Charlie" perfume from the mid-1970s until the early 1980s, and for her role as Tiffany Welles in Season 4 (19791980) of the ABC television drama "Charlie's Angels", replacing the departing Kate Jackson. She appeared in a total of 26 episodes of the series, before being replaced in Season 5 by model-actress Tanya Roberts. , Cheryl Ladd (born Cheryl Jean Stoppelmoor; July 12, 1951) is an American actress, singer, and author. Ladd is best known for her role as Kris Munroe in the ABC television series "Charlie's Angels", hired amid a swirl of publicity prior to its second season in 1977 to replace the departing Farrah Fawcett-Majors. Ladd remained with the show until its cancellation in 1981., Simone Kessell (born 1975) is a New Zealand-born Australian television actress known for her role as Lt. Alicia Washington in the short lived Fox science fiction television series "Terra Nova." In 2016, Kessell starred opposite Ray Winstone on the short-lived ABC prime-time television fantasy soap opera "Of Kings and Prophets.", Australia, officially the Commonwealth of Australia, is a country comprising the mainland of the Australian continent, the island of Tasmania and numerous smaller islands. It is the world's sixth-largest country by total area. The neighbouring countries are Papua New Guinea, Indonesia and East Timor to the north; the Solomon Islands and Vanuatu to the north-east; and New Zealand to the south-east. Australia's capital is Canberra, and its largest urban area is Sydney., California is the most populous state in the United States and the third most extensive by area. Located on the western (Pacific Ocean) coast of the U.S., California is bordered by the other U.S. states of Oregon, Nevada, and Arizona and shares an international border with the Mexican state of Baja California. The state capital is Sacramento. Los Angeles is California's most populous city, and the country's second largest after New York City. The state also has the nation's most populous county, Los Angeles County, and its largest county by area, San Bernardino County., Aaron Spelling (April 22, 1923  June 23, 2006) was an American film and television producer. Some of his successes include the TV programs "Charlie's Angels" (197681), "The Love Boat" (197786), "Dynasty" (198189), and "Beverly Hills, 90210" (19902000)., John Forsythe (born either John Lincoln Freund or Jacob Lincoln Freund; January 29, 1918  April 1, 2010) was an American stage, film/television actor, producer, narrator, drama teacher and philanthropist whose career spanned six decades. He also appeared as a guest on several talk and variety shows and as a panelist on numerous game shows., Farrah Fawcett (born Ferrah Leni Fawcett; February 2, 1947  June 25, 2009) was an American actress and artist. A four-time Emmy Award nominee and six-time Golden Globe Award nominee, Fawcett rose to international fame when she posed for her iconic red swimsuit poster  which became the best selling pin-up poster in history  and starred as private investigator Jill Munroe in the first season of the television series "Charlie's Angels" (19761977). In 1996, she was ranked No. 26 on "TV Guide" "50 Greatest TV stars of All-Time"., East Timor or Timor-Leste (Tetum: "Timór Lorosa'e"), officially the Democratic Republic of Timor-Leste, is a sovereign state in Maritime Southeast Asia. It comprises the eastern half of the island of Timor; the nearby islands of Atauro and Jaco; and Oecusse, an exclave on the northwestern side of the island surrounded by Indonesian West Timor. The country's size is about 15,410 km (5,400 sq mi)., New Zealand is an island nation in the southwestern Pacific Ocean. The country geographically comprises two main landmassesthat of the North Island, or Te Ika-a-Mui, and the South Island, or Te Waipounamuand numerous smaller islands. New Zealand is situated some east of Australia across the Tasman Sea and roughly south of the Pacific island areas of New Caledonia, Fiji, and Tonga. Because of its remoteness, it was one of the last lands to be settled by humans. During its long period of isolation, New Zealand developed a distinct biodiversity of animal, fungal and plant life. The country's varied topography and its sharp mountain peaks, such as the Southern Alps, owe much to the tectonic uplift of land and volcanic eruptions. New Zealand's capital city is Wellington, while its most populous city is Auckland., Indonesia (or ; Indonesian: ), officially the Republic of Indonesia, is a unitary sovereign state and transcontinental country located mainly in Southeast Asia with some territories in Oceania. Situated between the Indian and Pacific oceans, it is the world's largest island country, with more than seventeen thousand islands. At , Indonesia is the world's 14th-largest country in terms of land area and world's 7th-largest country in terms of combined sea and land area. It has an estimated population of over 260 million people and is the world's fourth most populous country, the most populous Austronesian nation, as well as the most populous Muslim-majority country. The world's most populous island of Java contains more than half of the country's population., Victoria Leigh Blum (born October 15, 1955), known by the stage name Tanya Roberts, is an American actress and producer. She is known for her role as Stacey Sutton in the James Bond film "A View to a Kill" (1985), and as Midge Pinciotti on "That '70s Show" (19982004)., Popstars is an international reality television franchise and a precursor to the "Idol" series. The series first began in New Zealand in 1999 when producer Jonathan Dowling formed the five member all-girl group TrueBliss. "Popstars" remains one of the most successful TV show formats of all time with the format being sold to more than 50 countries. The show was the inspiration for Simon Fuller's "Idols" franchise., Los Angeles (Spanish for "The Angels"), officially the City of Los Angeles and often known by its initials L.A., is the second-most populous city in the United States (after New York City), the most populous city in California and the county seat of Los Angeles County. Situated in Southern California, Los Angeles is known for its mediterranean climate, ethnic diversity, sprawling metropolis, and as a major center of the American entertainment industry. Los Angeles lies in a large coastal basin surrounded on three sides by mountains reaching up to and over ., Free-to-air (FTA) are television (TV) and radio services broadcast in clear (unencrypted) form, allowing any person with the appropriate receiving equipment to receive the signal and view or listen to the content without requiring a subscription, other ongoing cost or one-off fee (e.g. Pay-per-view). In the traditional sense, this is carried on terrestrial radio signals and received with an antenna., Katie Underwood (born 23 December 1975) is an Australian singer-songwriter, best known for being a member of Bardot, winners of the first Australian series of "Popstars" in 2000., Raymond Andrew "Ray" Winstone (born 19 February 1957) is an English film and television actor. He is mostly known for his "hard man" roles and Bet365 adverts beginning with his role as Carlin in the 1979 film "Scum" and Will Scarlet in the television series "Robin of Sherwood". He has also become well known as a voice over actor, and has recently branched out into film production. He has appeared in films such as "Cold Mountain", "Nil By Mouth", "King Arthur", "The Magic Roundabout", "The Departed", "Beowulf", "Indiana Jones and the Kingdom of the Crystal Skull", "Edge of Darkness", "The Sweeney" and "Noah"., Ian James Thorpe, (born 13 October 1982) is an Australian swimmer who specialises in freestyle, but also competes in backstroke and the individual medley. He has won five Olympic gold medals, the most won by any Australian, and with three gold and two silver medals, was the most successful athlete at the 2000 Summer Olympics. At the 2001 World Aquatics Championships, he became the first person to win six gold medals in one World Championship. In total, Thorpe has won eleven World Championship golds, the third-highest number of any swimmer. Thorpe was the first person to have been named "Swimming World" Swimmer of the Year four times, and was the Australian Swimmer of the Year from 1999 to 2003. His athletic achievements made him one of Australia's most popular athletes, and he was recognised as the Young Australian of the Year in 2000., Undercover Angels was a 2002 Australian television series produced by the Seven Network which imitated the American Charlie 's Angels series . It featured multiple Olympic and World champion swimmer Ian Thorpe , who acted as the mentor to three women ( Jackie O , Katie Underwood and Simone Kessell ) who performed good deeds for people in need . The show was first shown on 12 May , and was the fifth most watched television show in that week in Australia . Overall , it averaged 1.3 million viewers in its run of eleven episodes . The three `` angels '' travelled in Alfa Romeos performing deeds such as decorating a nursery for a young couple with newborn children , and finding a replacement puppy for children whose dog had been stolen . It was widely panned by media critics , with the Sydney Morning Herald television critic Ruth Ritchie declaring it `` the worst show in the history of the world '' . Thorpe , however , did not mind the criticism , pointing to the fact that he was satisfied that the show was in the minority of reality shows in which good behaviour was rewarded ., Charlie's Angels is an American crime drama television series that aired on ABC from September 22, 1976 to June 24, 1981, producing five seasons and 110 episodes. The series was created by Ivan Goff and Ben Roberts and was produced by Aaron Spelling. It plots the adventures of three women working in a private detective agency in Los Angeles, California, and initially starred Kate Jackson, Farrah Fawcett, and Jaclyn Smith in the leading roles, with David Doyle co-starring as a sidekick to the three women and John Forsythe providing the voice of their boss. Later additions to the cast were Cheryl Ladd, Shelley Hack, and Tanya Roberts., The Seven Network (commonly known as Channel Seven or simply Seven) is an Australian commercial free-to-air television network. It is owned by Seven West Media Limited, and is one of five main free-to-air television networks in Australia., Solomon Islands is a sovereign country consisting of six major islands and over 900 smaller islands in Oceania lying to the east of Papua New Guinea and northwest of Vanuatu and covering a land area of . The country's capital, Honiara, is located on the island of Guadalcanal. The country takes its name from the Solomon Islands archipelago, which is a collection of Melanesian islands that also includes the North Solomon Islands (part of Papua New Guinea), but excludes outlying islands, such as Rennell and Bellona, and the Santa Cruz Islands., Lucy Kate Jackson (born October 29, 1948) is an American actress, director and producer, known for her television roles as Sabrina Duncan in the 1970s series "Charlie's Angels" (197679) and Amanda King in the 1980s series "Scarecrow and Mrs. King" (198387). Her film roles include "Making Love" (1982) and "Loverboy" (1989). She is a three-time Emmy Award nominee and four-time Golden Globe Award nominee., The 2000 Summer Olympic Games, officially known as the Games of the XXVII Olympiad and commonly known as Sydney 2000 or the Millennium Olympic Games/Games of the New Millennium, were an international multi-sport event which was held between 15 September and 1 October 2000 in Sydney, New South Wales, Australia. It was the second time that the Summer Olympics were held in Australia, and also the Southern Hemisphere, the first being in Melbourne, Victoria, in 1956., Subject: undercover angels, Relation: genre, Options: (A) animal (B) country (C) crime (D) drama (E) entertainment (F) game (G) history (H) james (I) marketing (J) poster (K) radio (L) reality television (M) science (N) science fiction (O) spelling (P) sport (Q) television (R) tv show (S) urban (T) western (U) will

SOLUTION:
reality television