query: field_of_work carl pomerance
supports: In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. ""("n") = 2"n". The colonial colleges are nine institutions of higher education chartered in the American Colonies before the United States of America became a sovereign nation after the American Revolution. These nine have long been considered together, notably in the survey of their origins in the 1907 "The Cambridge History of English and American Literature". Seven of the nine colonial colleges are part of the Ivy League athletic conference: Harvard, Yale, Penn, Princeton, Columbia, Brown, and Dartmouth. (The eighth member of the Ivy League, Cornell University, was founded in 1865.) Harvard University is a private Ivy League research university in Cambridge, Massachusetts, established in 1636, whose history, influence, and wealth have made it one of the world's most prestigious universities. Brown University is a private Ivy League research university in Providence, Rhode Island, United States, founded in 1764 as "The College in the English Colony of Rhode Island and Providence Plantations." Brown is the seventh-oldest institution of higher education in the United States and one of the nine Colonial Colleges established before the American Revolution. Higher education, post-secondary education, or third level education is an optional final stage of formal learning that occurs after completion of secondary education. Often delivered at universities, academies, colleges, seminaries, and institutes of technology, higher education is also available through certain college-level institutions, including vocational schools, trade schools, and other career colleges that award academic degrees or professional certifications. Tertiary education at non-degree level is sometimes referred to as further education or continuing education as distinct from higher education. The University of Georgia, founded in 1785, also referred to as UGA or simply Georgia, is an American public Land-grant, Regional Sun Grant, National Sea Grant, and National Space Grant research university. Its primary location is a campus adjacent to the college town of Athens, Georgia, approximately an hour's drive from the global city of Atlanta. It is a flagship university that is ranked tied for 18th overall among all public national universities in the 2017 "U.S. News & World Report" rankings. The university is classified in the highest ranking, "R-1: ", with the Carnegie Classification of Institutions of Higher Education classifying the student body as "More Selective," its most selective admissions category. The university has been labeled one of the "Public Ivies," a publicly funded university considered to provide a quality of education comparable to those of the Ivy League.  St. Louis is an independent city and major U.S. port in the State of Missouri, built along the western bank of the Mississippi River, on the border with Illinois. The city has an estimated 2015 population of 315,685, and is the cultural and economic center of the Greater St. Louis area (home to 2,916,447 people), making it the largest metropolitan area in Missouri and the 19th-largest in the United States. In public relations and communication science, publics are groups of individual people, and the public (a.k.a. the general public) is the totality of such groupings. This is a different concept to the sociological concept of the Öffentlichkeit or public sphere. The concept of a public has also been defined in political science, psychology, marketing, and advertising. In public relations and communication science, it is one of the more ambiguous concepts in the field. Although it has definitions in the theory of the field that have been formulated from the early 20th century onwards, it has suffered in more recent years from being blurred, as a result of conflation of the idea of a public with the notions of audience, market segment, community, constituency, and stakeholder. Eleazar Wheelock (April 22, 1711  April 24, 1779) was an American Congregational minister, orator, and educator in Lebanon, Connecticut, for 35 years before founding Dartmouth College in New Hampshire. He had tutored Samson Occom, a Mohegan who became a Presbyterian minister and the first Native American to publish writings in English. Before founding Dartmouth, Wheelock had founded and run the Moor's Charity School in Connecticut to educate Native Americans. The college was primarily for the sons of English colonists. Missouri (see pronunciations) is a state in the Midwestern region of the United States, achieving statehood in 1821. With over six million residents, it is the eighteenth most populous state and host to the mean center of United States population. The largest urban areas are St. Louis, Kansas City, Springfield, and Columbia. The capitol is in Jefferson City on the Missouri River. The state is the twenty-first most extensive by area and is geographically diverse. The Northern Plains were once covered by glaciers, then tallgrass prairie, and now the deep soils yield great agricultural productivity. In the South are the Ozarks, a forested highland, providing timber, minerals, and recreation. The Mississippi River forms the eastern border of the state, eventually flowing into the swampy Missouri Bootheel. Carl Bernard Pomerance ( born in 1944 in Joplin , Missouri ) is an American number theorist . He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least 7 distinct prime factors . He immediately joined the faculty at the University of Georgia , becoming full professor in 1982 . He subsequently worked at Lucent Technologies for a number of years , and then became a distinguished Professor at Dartmouth College . A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking.  A global city, also called world city or sometimes alpha city or world center, is a city generally considered to be an important node in the global economic system. The concept comes from geography and urban studies, and the idea that globalization can be understood as largely created, facilitated, and enacted in strategic geographic locales according to a hierarchy of importance to the operation of the global system of finance and trade. Athens (formally known as Athens-Clarke County) is a consolidated citycounty in the U.S. state of Georgia, in the northeastern part of the state, comprising the former city of Athens proper (the county seat) and Clarke County. The University of Georgia, the state's flagship public research university, is located in this college town, and contributed to its initial growth. In 1991, after a vote the preceding year, the original city abandoned its charter to form a unified government with Clarke County, referred to jointly as Athens-Clarke County. As of the 2010 census, the consolidated city-county (including all of Athens-Clarke County except Winterville and a portion of Bogart) had a total population of 115,452; all of Clarke County had a population of 116,714. Athens is the sixth-largest city in Georgia, and the principal city of the Athens-Clarke County, Georgia Metropolitan Statistical Area, which had a population of 192,541 as of the 2010 census. Athens-Clarke County has the smallest geographical area of a county in Georgia. In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicities; the process of determining these factors is called integer factorization. The fundamental theorem of arithmetic says that every positive integer has a single unique prime factorization. Kansas is a U.S. state located in the Midwestern United States. Its capital is Topeka and its largest city is Wichita. Kansas is named after the Kansa Native American tribe, which inhabited the area. The tribe's name (natively "") is often said to mean "people of the wind" or "people of the south wind", although this was probably not the term's original meaning. For thousands of years, what is now Kansas was home to numerous and diverse Native American tribes. Tribes in the eastern part of the state generally lived in villages along the river valleys. Tribes in the western part of the state were semi-nomadic and hunted large herds of bison. 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). Dartmouth College is a private Ivy League research university in Hanover, New Hampshire, United States. Established in 1769 by Eleazar Wheelock, Dartmouth is one of the nine colonial colleges chartered before the American Revolution. The American Revolution was a political upheaval that took place between 1765 and 1783 during which colonists in the Thirteen American Colonies rejected the British monarchy and aristocracy, overthrew the authority of Great Britain, and founded the United States of America. The Missouri River is the longest river in North America. Rising in the Rocky Mountains of western Montana, the Missouri flows east and south for before entering the Mississippi River north of St. Louis, Missouri. The river takes drainage from a sparsely populated, semi-arid watershed of more than half a million square miles (1,300,000 km), which includes parts of ten U.S. states and two Canadian provinces. When combined with the lower Mississippi River, it forms the world's fourth longest river system. The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism. In mathematics, a divisor of an integer formula_1, also called a factor of formula_1, is an integer formula_3 that may be multiplied by some other integer to produce formula_1. In this case one says also that formula_1 is a multiple of formula_6 An integer formula_1 is divisible by another integer formula_3 if formula_3 is a divisor of formula_1; this implies dividing formula_1 by formula_3 leaves no remainder. Hanover is a town in Grafton County, New Hampshire, United States, along the Connecticut River. The population was 11,260 at the 2010 census. CNN and "Money" magazine rated Hanover the sixth best place to live in America in 2011, and the second best in 2007. "This just might be the best college town," read a headline in a story in the January / February 2017 issue of "Yankee".  The Mississippi River is the chief river of the largest drainage system on the North American continent. Flowing entirely in the United States (although its drainage basin reaches into Canada), it rises in northern Minnesota and meanders slowly southwards for to the Mississippi River Delta at the Gulf of Mexico. With its many tributaries, the Mississippi's watershed drains all or parts of 31 U.S. states and 2 Canadian provinces between the Rocky and Appalachian Mountains. The Mississippi ranks as the fourth longest and fifteenth largest river in the world by discharge. The river either borders or passes through the states of Minnesota, Wisconsin, Iowa, Illinois, Missouri, Kentucky, Tennessee, Arkansas, Mississippi, and Louisiana. In number theory, the aliquot sum "s"("n") of a positive integer "n" is the sum of all proper divisors of "n", that is, all divisors of "n" other than "n" itself. The aliquot sums of perfect, deficient, and abundant numbers are equal to, less than, and greater than the number itself respectively. The aliquot sequence is the sequence obtained by repeatedly applying the aliquot sum function "s". The aliquot sum function is also referred to as the restricted divisor function.
candidates: advertising classification communication education english geography globalization marketing mathematics minister number theory political science research river science technology trade training united states of america
answer: number theory