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1. web.math.ku.dk › ~risager › introtalIntroduction to number theory - ku

   web.math.ku.dk › ~risager › introtal

   1.2 Euclidean division and greatest common divisor 7 a unique solution q = q0 1, r =b r0to a =bq+r with 0 r <jbj.We may therefore assume a;b >0. If a;b >0 consider Q =fn 2Zjn 0;a bn 0g:

2. www.math.gordon.edu › ntic › nticNumber Theory - Gordon College

   www.math.gordon.edu › ntic › ntic

   number theory is the queen of mathematics (hence the title of [E.5.4]). If you don’t yet know why that might be the case, you are in for a treat. Number theory was (and is still occasionally) called ‘the higher arithmetic’, and that is truly where it starts. Even a small child understands that there is

3. open.umn.edu › opentextbooks › textbooksAn Introduction to the Theory of Numbers - Open Textbook Library

   open.umn.edu › opentextbooks › textbooks

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   This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations ...

4. web.mit.edu › neboat › PublicNumber Theory I - MIT - Massachusetts Institute of Technology

   web.mit.edu › neboat › Public

   A number p > 1 with no positive divisors other than 1 and itself is called a prime. Every other number greater than 1 is called composite. For example, 2, 3, 5, 7, 11, and 13 are all prime, but 4, 6, 8, and 9 are composite. The number 1 is considered neither prime nor composite. This is just a matter of definition, but reflects the fact that ...

5. www.math.brown.edu › ~jhs › frintch1ch6What Is Number Theory? - Brown University

   www.math.brown.edu › ~jhs › frintch1ch6

   What Is Number Theory? Number theory is the study of the set of positive whole numbers 1;2;3;4;5;6;7;:::; which are often called the set of natural numbers. We will especially want to study the relationships between different sorts of numbers. Since ancient times, people have separated the natural numbers into a variety of different types. Here ...

6. artofproblemsolving.com › articles › filesNumber Theory - Art of Problem Solving

   artofproblemsolving.com › articles › files

   Theorem 1.3. (Euclid) There exist an infinite number of primes. Proof. Suppose that there are a finite number of primes, say p 1, p 2, ..., p n. Let N = p 1p 2 ···p n + 1. By the fundamental theorem of arithmetic, N is divisible by some prime p. This prime p must be among the p i, since by

7. www.math.brown.edu › IHM2020NumberTheoryUnit4Introduction to Higher Mathematics Unit #4: Number Theory

   www.math.brown.edu › IHM2020NumberTheoryUnit4

   2 1. Number Theory — Lecture #1 the divisors of 28 are 1, 2, 4, 7, and 14, and 1+2+4+7+14 = 28: We will encounter many of these types of numbers in our excursion through the Theory of Numbers. Some Typical Number Theoretic Questions The main goal of number theory is to discover interesting and unexpected relation-