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4 Number Theory I: Prime Numbers - University of Pennsylvania

Last edited February 11, 20164 Number Theory I: Prime NumbersNumber Theory is the mathematical study of the natural Numbers , the positivewhole Numbers such as 2, 17, and 123. Despite their ubiquity and apparent sim-plicity, the natural integers are chock-full of beautiful ideas and open primary focus of Number Theory is the study of Prime Numbers , which can beviewed as the elementary building blocks of all Number TheoryThe natural Numbers are those basic abstraction of quantity we first learn aboutas children; in particular they are the positive whole Numbers :N={1,2,3,..}.(36)Although simple in some sense, the patterns and relationships that appearamong these Numbers have intrigued and challenged generations of the mathe-maticians. Despite hundreds of years of progress, there is still many areas weknow very little about. We begin by very briefly considering three kinds ofproblems that arise in Number Theory , and which highlight di erent aspects ofthe Remainders of Large NumbersSince elementary school, readers of these notes have known how to divide twointegers and calculate whole Numbers plus remainders.

viewed as the elementary building blocks of all numbers. 4.1 Number Theory The natural numbers are those basic abstraction of quantity we first learn about ... Aside from his many contributions to geometry, Euclid also made important contributions to our understanding of numbers. In partic-ular, Euclid showed that for any finite number n ...

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