Fundamentals of Number TheoryBasic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition. |
Contents
Introduction | 1 |
Unique Factorization and the | 31 |
Congruences and the Ring | 47 |
Copyright | |
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a₁ algebraic number algorithm ax² b₁ best approximations c₁ Cauchy sequence Chinese remainder theorem coefficients congruence continued fraction converges d₁ Deduce defined Diophantine equation Dirichlet elements equation x² equivalent Euclidean domain Euler example expansion Fermat finite function Gauss gives Hence Hint implies inequality Legendre symbol li(x linear log log log² m₁ mathematics mod 2º multiplicative n₁ nonresidue nonzero number theory obtain odd prime p-adic numbers P₁ Pell equation polynomial positive integers positive prime prime divisor prime number prime number theorem primitive root Problem proof properties proved quadratic reciprocity quadratic residue r₁ rational numbers real numbers reduced residue system relatively prime representation residue classes residue classes mod result Ring Section Show smallest positive solvable square-free squares Suppose unique factorization values x₁