A guide to elementary number theory [[electronic resource] /] / Underwood Dudley

• Record Nr.: UNINA9910465224303321
• Autore: Dudley Underwood
• Pubbl/distr/stampa: [Washington, D.C.], : Mathematical Association of America, c2009
• ISBN: 0-88385-918-1
• Descrizione fisica: 1 online resource (x, 141 pages) : digital, PDF file(s)
• Collana: Dolciani mathematical expositions ; ; no. 41; MAA guides ; ; no. 5
• Disciplina: 512.7/2
• Soggetti: Number theory; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Includes index.
• Nota di contenuto: Greatest common divisors -- Unique factorization -- Linear Diophantine equations -- Congruences -- Linear congruences -- The Chinese remainder theorem -- Fermat's theorem -- Wilson's theorem -- The number of divisors of an integer -- The sum of the divisors of an integer -- Amicable numbers -- Perfect numbers -- Euler's theorem and function -- Primitive roots and orders -- Decimals -- Quadratic congruences -- Gauss's lemma -- The quadratic reciprocity theorem -- The Jacobi symbol -- Pythagorean triangles -- x⁴ + y⁴ [not equal] z⁴ -- Sums of two squares -- Sums of three squares -- Sums of four squares -- Waring's problem -- Pell's equation -- Continued fractions -- Multigrades -- Carmichael numbers -- Sophie Germain primes -- The group of multiplicative functions -- Bounds for [pi](x) -- The sum of the reciprocals of the primes -- The Riemann hypothesis -- The prime number theorem -- The abc conjecture -- Factorization and testing for primes -- Algebraic and transcendental numbers -- Unsolved problems.
• Sommario/riassunto: "A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through traditional texts, some of which approach 500 ; pages in length. It will be especially useful to graduate students preparing for qualifying exams. Though Plato did not quite say, "He is unworthy of the name of man who does not know which integers are the sums of two squares," he came close. This guide can make everyone more worthy"--P. [4] of cover.