Elementary Theory of Numbers
Superb introduction for readers with limited formal mathematical training. Topics include Euclidean algorithm and its consequences, congruences, powers of an integer modulo m, continued fractions, Gaussian integers, Diophantine equations, more. Carefully selected problems included throughout, with answers. Only high school math needed. Bibliography.
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algebra ANALYSIS applications arithmetic assertion Bibliography CALCULUS CALCULUS OF VARIATIONS Classic coefficients common divisor common factor consider continued fraction expansion convergent deduce DIFFERENTIAL EQUATIONS digits Diophantine equations divides divisible elements equation x2 equivalent Euclidean algorithm exactly example finite following theorem function Gaussian integers Gaussian primes geometry hence implies Index inequality INTRODUCTION irrational number Lagrange's theorem mathematics mechanics mod 9 mod mn modulo multiplication natural numbers nonnegative norm number theory obtain odd prime ORDINARY DIFFERENTIAL EQUATIONS Pell's equation period length PHYSICS polynomials positive integer positive solution prime numbers primitive root problems Proof properties prove quadratic residue quantum rational integers rational number rational prime real number reduced residue system relatively prime representation residue classes residue system mod Section sequence Show simple continued fraction solvable solved square Suppose text covers Theorem 1-1 theory of numbers tion true unique factori2ation theorem