field_of_work carl pomerance
Athens ( formally known as Athens - Clarke County ) is a consolidated city  county 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 ___MASK79___ 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 . Hanover is a town in Grafton County , New Hampshire , United States , along the Connecticut ___MASK32___ . 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 ". 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 ___MASK32___ valleys . Tribes in the western part of the state were semi - nomadic and hunted large herds of bison . The colonial colleges are nine institutions of higher ___MASK100___ chartered in the American Colonies before the ___MASK70___ 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 ___MASK49___ of English and American ___MASK50___ ". 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 .) Eleazar Wheelock ( April 22 , 1711  April 24 , 1779 ) was an American Congregational ___MASK75___ , 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 ___MASK75___ 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 . 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 ___MASK33___ and urban studies , and the idea that ___MASK92___ 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 ___MASK6___ and trade . The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher ___MASK100___ 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 . St . Louis is an independent city and major U . S . port in the State of Missouri , built along the western bank of the Mississippi ___MASK32___ , 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 ___MASK96___ ___MASK4___ , 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 ___MASK4___ , ___MASK27___ , marketing , and advertising . In public relations and ___MASK96___ ___MASK4___ , 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 . Harvard University is a private Ivy League ___MASK79___ university in Cambridge , Massachusetts , established in 1636 , whose history , influence , and wealth have made it one of the world ' s most prestigious universities . In ___MASK13___ , 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 ". Higher ___MASK100___ , post - secondary ___MASK100___ , or third level ___MASK100___ is an optional final stage of formal learning that occurs after completion of secondary ___MASK100___ . Often delivered at universities , academies , colleges , seminaries , and institutes of technology , higher ___MASK100___ is also available through certain college - level institutions , including vocational schools , ___MASK56___ schools , and other career colleges that award academic degrees or professional certifications . Tertiary ___MASK100___ at non - degree level is sometimes referred to as further ___MASK100___ or continuing ___MASK100___ as distinct from higher ___MASK100___ . 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 ___MASK32___ . 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 ___MASK32___ forms the eastern border of the state , eventually flowing into the swampy Missouri Bootheel . The Missouri ___MASK32___ is the longest ___MASK32___ in North America . Rising in the Rocky Mountains of western Montana , the Missouri flows east and south for before entering the Mississippi ___MASK32___ north of St . Louis , Missouri . The ___MASK32___ 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 ___MASK32___ , it forms the world ' s fourth longest ___MASK32___ system . In ___MASK13___ , 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 . 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 ___MASK79___ university is a university that expects all its tenured and tenure - track faculty to continuously engage in ___MASK79___ , 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 ___MASK79___ and the prestige of their brand names . On the one hand , ___MASK79___ 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 ___MASK79___ universities are overly academic and fail to provide vocational ___MASK10___ with immediate " real world " applications ; but many employers value degrees from ___MASK79___ universities because they know that such coursework develops fundamental skills like critical thinking . Brown University is a private Ivy League ___MASK79___ 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 . 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 ___MASK70___ . In ___MASK26___ , 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 . Dartmouth College is a private Ivy League ___MASK79___ 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 . In ___MASK13___ , 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 . 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 ___MASK79___ 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 ___MASK88___ 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 . ___MASK13___ 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 ). The Mississippi ___MASK32___ is the chief ___MASK32___ 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 ___MASK32___ 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 ___MASK32___ in the world by discharge . The ___MASK32___ either borders or passes through the states of Minnesota , Wisconsin , Iowa , Illinois , Missouri , Kentucky , Tennessee , Arkansas , Mississippi , and Louisiana .