Introduction to the Theory of NumbersCourier Corporation, 2008 M01 1 - 459 pages Starting with the fundamentals of number theory, this text advances to an intermediate level. Author Harold N. Shapiro, Professor Emeritus of Mathematics at New York University's Courant Institute, addresses this treatment toward advanced undergraduates and graduate students. Selected chapters, sections, and exercises are appropriate for undergraduate courses. The first five chapters focus on the basic material of number theory, employing special problems, some of which are of historical interest. Succeeding chapters explore evolutions from the notion of congruence, examine a variety of applications related to counting problems, and develop the roots of number theory. Two "do-it-yourself" chapters offer readers the chance to carry out small-scale mathematical investigations that involve material covered in previous chapters. |
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0(x log a₁ abelian group arithmetic function arithmetic progressions assertion b₁ Bertrand's Postulate c₁ character modulo congruence consider convolution Corollary coset defined Definition denote derivation direct product Dirichlet Disquisitiones Arithmeticae divides divisible element equations equivalent Erdos estimate Euler EXERCISES exists Fermat's following lemma following theorem formula Gauss given integer greatest common divisor H₁ hence identity implies induction integer coefficients Legendre Lo(x log log lower bound m₁ Mathematical mod pº nonresidue notation number of positive number of solutions obtain odd perfect number odd prime ord g p=B(mod p₁ polynomial positive integers Prime Number Theorem problem Prove provides q₁ quadratic nonresidue Quadratic Reciprocity Law quadratic residue real number reduced residue system relatively prime representation residue classes Show solutions modulo squarefree sufficiently large theory Unique Factorization Theorem x₁ yields Σ Σ ΣΣ