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
Primes and Their Distribution
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9 mod Arithmetica asserts assume coefficients composite numbers congruence x2 congruent modulo conjecture consecutive digits Diophantine equation Diophantus divides Division Algorithm equal Euclid's Euclidean Algorithm Euler Euler's Criterion example Fermat's Theorem Fibonacci numbers finite number form 4k formula four squares Gauss Goldbach's Conjecture greatest common divisor hence Hint implies incongruent solutions induction infinitely many primes integers less Legendre symbol Lemma linear congruence mathematician mathematics Mersenne Mersenne primes modp multiplicative function number of primes number theory obtain odd integer odd prime pairs perfect square positive divisors positive integer powers prime divisor prime factorization prime number primitive Pythagorean triple primitive root problem Proof Prove Pythagorean triangle Pythagorean triple quadratic congruence quadratic nonresidue Quadratic Reciprocity Law quadratic residue relatively prime remainder representation result satisfying simple continued fraction solvable Theorem 9-2 triangular numbers values Verify whence Wilson's Theorem x2 a mod