Elementary Introduction to Number Theory |
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Contents
PRELIMINARY CONSIDERATIONS | 1 |
DIVISIBILITY PROPERTIES OF INTEGERS | 31 |
PRIME NUMBERS | 59 |
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a₁ ap(m b₁ canonical representation Chinese remainder theorem common divisor common multiple complete residue system completely multiplicative congruent modulo contradiction convergent Corollary divided divisible equation example exist integers Find following theorem form 4k formula function given congruence greatest common divisor guess hence Hint I₁ implies incongruent solutions modulo infinitely many primes integers q integral squares least element log Pn m₁ mathematical induction notation number of positive obtain odd prime Pn+1 polynomial positive divisors preceding theorem primitive Pythagorean triplet primitive root modulo proof of Theorem prove Pythagorean triplet quadratic nonresidue quadratic residue modulo r₁ real number reduced residue system relatively prime residue system modulo result of Exercise s₁ simple continued fraction solution of f(x solvable solving Suppose theory of numbers unique values well-ordering principle Wilson's theorem zero