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 to1, 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, and2048 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: The Monster Energy NASCAR Cup Series is the top racing series of the National Association for Stock Car Auto Racing (NASCAR). It is named for the current sponsor, Monster Energy, but has been known by other names in the past. The series began in 1949 as the Strictly Stock Series, and from 1950 to 1970 it was known as the Grand National Series. In 1971, when the series began leasing its naming rights to the R. J. Reynolds Tobacco Company, it was referred to as the Winston Cup Series. A similar deal was made with Nextel in 2003, and it became the Nextel Cup Series (20042007). Sprint acquired Nextel in 2005, and in 2008 the series was renamed the Sprint Cup Series, which lasted until 2016. In December 2016, it was announced that Monster Energy would become the new title sponsor starting in 2017., Monster Energy is an energy drink introduced by Hansen Natural Corp. (HANS) in April 2002. The regular flavor comes in a black can with a green, torn M shaped logo. The company is also known for supporting many extreme sports events such as UFC, BMX, Motocross, Speedway, skateboarding and snowboarding, as well as eSports. In addition, Monster Energy promotes a number of music bands around the world, like Asking Alexandria, The Word Alive, Maximum the Hormone and Five Finger Death Punch. Monster currently sponsors the Monster Energy NASCAR Cup Series., Ginn Racing was a NASCAR Nextel Cup Series team based in Mooresville , North Carolina , near the sport 's hub in Charlotte . Its principal owners in its final season , 2007 , were resort and real - estate developer Bobby Ginn ( the Ginn family Owned 80 % ) and longtime team director Jay Frye ( 20 % ) . The team 's original name was MB2 Motorsports , formed by the last names of the team owners Read Morton , Tom Beard , and Nelson Bowers . Bowers was the longest tenured of the original owners , and the listed owner of the teams ' entries when Bobby Ginn bought out the team . The Valvoline corporation co-owned the # 10 ( later the # 14 ) car with the principal owners from 2001 to 2005 as MBV Motorsports , while the # 36 entry ( later the # 13 ) was co-owned by Centrix Financial , LLC owner Robert Sutton as MB Sutton Motorsports in 2005 ., The 2010 United States Census, (known as "Census 2010"), is the twenty-third and currently most recent United States national census. National Census Day, the reference day used for the census, was April 1, 2010. As part of a drive to increase the count's accuracy, 635,000 temporary enumerators were hired. The population of the United States was counted as 308,745,538, a 9.7% increase from the 2000 Census., iRacing is a subscription based racing simulation released by iRacing.com Motorsport Simulations in 2008. Official races, special events, league races, and practice sessions are all hosted on the service's servers. The service simulates realistic cars, tracks, and racing events, and enforcing rules of conduct modeled on real auto racing events., North Carolina is a state in the southeastern region of the United States. The state borders South Carolina and Georgia to the south, Tennessee to the west, Virginia to the north, and the Atlantic Ocean to the east. North Carolina is the 28th most extensive and the 9th most populous of the U.S. states. The state is divided into 100 counties. The capital is Raleigh. The most populous municipality is Charlotte, and it is the second largest banking center in the United States after New York City., Mooresville is a town in southern Iredell County, North Carolina, USA. It is in the Metrolina metro area, and is on Lake Norman. The population was 32,711 at the 2010 United States Census. It is located approximately 25 miles north of Charlotte., Edward Robert "Bobby" Ginn III is the Chairman and CEO representing several of the Ginn Family Companies, over 200 family owned companies from developing to the management of these companies, and partner of a merged NASCAR Nextel Cup team Ginn Racing (formerly MB2 Motorsports, which he purchased from MB2 owner Nelson Bowers, Jr. in 2006)., William Henry Getty "Bill" France (September 26, 1909 June 7, 1992), also known as Bill France Sr. or Big Bill, was an American racing driver. He is best known for co-founding and managing NASCAR, a sanctioning body of US-based stock car racing., The Autodromo Hermanos Rodriguez is a race track in Mexico City, Mexico, named after the racing drivers Ricardo and Pedro Rodriguez. The circuit got its name shortly after it opened when Ricardo Rodriguez died in practice for the non-Championship 1962 Mexican Grand Prix. Ricardo's brother Pedro also lost his life behind the wheel nine years later., The NASCAR Camping World Truck Series (formerly the NASCAR SuperTruck Series presented by Craftsman and the NASCAR Craftsman Truck Series) is a pickup truck racing series owned and operated by the National Association for Stock Car Auto Racing, and is the only series in all of NASCAR to race modified production pickup trucks. The series is one of three national divisions of NASCAR, ranking as the third tier behind the second-tier Xfinity Series and the top level Monster Energy NASCAR Cup Series. Camping World has served as the title sponsor since 2009; it replaced Craftsman, who served in that role from 1996 through 2008., Mexico (, modern Nahuatl ), officially the United Mexican States, is a federal republic in the southern half of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatemala, Belize, and the Caribbean Sea; and to the east by the Gulf of Mexico. Covering almost two million square kilometers (over 760,000sqmi), Mexico is the sixth largest country in the Americas by total area and the 13th largest independent nation in the world. With an estimated population of over 120 million, it is the eleventh most populous country and the most populous Spanish-speaking country in the world while being the second most populous country in Latin America. Mexico is a federation comprising 31 states and a federal district that is also its capital and most populous city. Other metropolises include Guadalajara, Monterrey, Puebla, Toluca, Tijuana and Leon., The National Association for Stock Car Auto Racing (NASCAR) is an American family-owned and operated business venture that sanctions and governs multiple auto-racing sports events. Bill France Sr. founded the company in 1948 and his grandson Brian France became its CEO in 2003. NASCAR is motorsport's preeminent stock-car racing organization. The three largest racing-series sanctioned by this company are the Monster Energy NASCAR Cup Series, the Xfinity Series, and the Camping World Truck Series. The company also oversees NASCAR Local Racing, the Whelen Modified Tour, the Whelen All-American Series, and the NASCAR iRacing.com Series. NASCAR sanctions over 1,500 races at over 100 tracks in 39 of the 50 US states as well as in Canada. NASCAR has presented exhibition races at the Suzuka and Motegi circuits in Japan, the Autodromo Hermanos Rodriguez in Mexico, and the Calder Park Thunderdome in Australia., Lake Norman, created between 1959 and 1964 as part of the construction of the Cowans Ford Dam by Duke Energy, is the largest man made body of fresh water located in North Carolina., Brian France (born August 2, 1962) is an American businessman who is the current CEO and Chairman of NASCAR, taking over the position from his father, Bill France Jr., in 2003. "Time Magazine" named him one of the "100 Most Influential of the Century" in 2006 and he was named one of the five most powerful sports executives by "The Sporting News" in 2005., The NASCAR Whelen Modified Tour (NWMT) (previously the NASCAR Winston Modified Tour and NASCAR Featherlite Modified Series from 1985 until 2005) is a stock car racing series owned and operated by NASCAR in the Modified Division. The Modified Division is NASCAR's oldest division, and is the only open-wheeled division that NASCAR sanctions. NASCAR Whelen Modified Tour events are mainly held in the northeastern United States, but the 2007 and 2008 tours expanded to the Midwest with the addition of a race in Mansfield, Ohio. The tour races primarily on short oval paved tracks, but the NWMT also has made appearances at larger ovals and road courses. , Camping World is an American corporation specializing in selling recreational vehicles, recreational vehicle parts, and recreational vehicle service. They also sell supplies for camping. The company has its headquarters in Lincolnshire, Illinois. In October 2016 it became a publicly traded company when it raised $251 million in an IPO. Camping World operates 120 retail/service locations in 36 states, and also sells goods through mail order and online. It claims to be the world's largest supplier of RV parts and supplies. The company is also the title sponsor for the NASCAR Camping World East Series, NASCAR Camping World West Series, and NASCAR Camping World Truck Series. Recently, it has become the title sponsor of the Camping World Stadium, home of the Orlando City soccer team., Subject: ginn racing, Relation: inception, Options: (A) 1 (B) 100 (C) 120 (D) 14 (E) 1909 (F) 1948 (G) 1949 (H) 1950 (I) 1959 (J) 1962 (K) 1964 (L) 1970 (M) 1985 (N) 1992 (O) 1996 (P) 2 (Q) 20 (R) 200 (S) 2001 (T) 2004 (U) 2005 (V) 2006 (W) 2007 (X) 2008 (Y) 2009 (Z) 2010 ([) 2016 (\) 25 (]) 500 (^) 7 (_) 760 (') april 2002

SOLUTION: 1996

PROBLEM: Context: A pen name ("nom de plume", or "literary double") is a pseudonym (or, in some cases, a variant form of a real name) adopted by an author and printed on the title page or by-line of his or her works in place of their "real" name. A pen name may be used to make the author's name more distinctive, to disguise his or her gender, to distance an author from some or all of his or her previous works, to protect the author from retribution for his or her writings, to combine more than one author into a single author, or for any of a number of reasons related to the marketing or aesthetic presentation of the work. The author's name may be known only to the publisher, or may come to be common knowledge., The Garden Murder Case ( first published in 1935 ) is the ninth in a series of mystery novels by S. S. Van Dine about fictional detective Philo Vance ., S. S. Van Dine (also styled S.S. Van Dine) is the pseudonym used by American art critic Willard Huntington Wright (October 15, 1888 April 11, 1939) when he wrote detective novels. Wright was an important figure in avant-garde cultural circles in pre-World War I New York, and under the pseudonym (which he originally used to conceal his identity) he created the once immensely popular fictional detective Philo Vance, a sleuth and aesthete who first appeared in books in the 1920s, then in movies and on the radio., Philo Vance is a fictional character featured in 12 crime novels written by S. S. Van Dine (the pen name of Willard Huntington Wright), published in the 1920s and 1930s. During that time, Vance was immensely popular in books, movies, and on the radio. He was portrayed as a stylish, even foppish dandy, a New York "bon vivant" possessing a highly intellectual bent. The novels were chronicled by his friend Van Dine (who appears as a kind of Dr. Watson figure in the books as well as being the author)., Subject: the garden murder case, Relation: author, Options: (A) one (B) willard huntington wright

SOLUTION:
willard huntington wright