Elementary number theory
"Elementary Number Theory," Sixth Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton's engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.
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Some Preliminary Considerations
Divisibility Theory in the Integers
Chapter 3 Primes and Their Distribution
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9 mod arithmetic asserts assume congruence x2 congruent modulo conjecture consecutive convergents digits Diophantine equation divides equal equation x2 establish Euclidean Algorithm Euler Euler's Criterion example Fermat number Fermat's Theorem Fibonacci numbers finite number form 4k formula Gauss gcd(a gcd(fl given greatest common divisor hence Hint implies induction inequality infinitely many primes integers less irrational number Legendre symbol Lemma linear congruence mathematician mathematics Mersenne primes mod 9 modp nonresidue number of primes number theory obtain odd integer odd prime pair perfect number perfect square positive divisors positive integer positive solution powers prime divisor prime factorization prime number primitive Pythagorean triple primitive root problem Proof Prove pseudoprime Pythagorean triple quadratic congruence quadratic nonresidue quadratic residue rational number relatively prime representation result satisfying sequence solution of x2 solvable Theorem 8-1 triangular numbers twin primes values Verify whence Wilson's Theorem