By Underwood Dudley

ISBN-10: 071670076X

ISBN-13: 9780716700760

Designed for a primary direction in quantity conception with minimum must haves, the e-book is designed to stimulates interest approximately numbers and their homes. comprises virtually 1000 inventive workouts and difficulties.

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Additional info for Elementary Number Theory (Series of Books in the Mathematical Sciences)

Sample text

Of complex numbers we can associate a formal power series a(X) L n=O Equality of formal power series means term-by-term equality.

41. • ~) k be a positive integer. obtained when each xi The set of ordered k-tuples runs over a complete set of residues (mod n) is called a k-residue system (mod n). • x k ' n) reduced k-residue system (mod n). system (mod n) is the union of If din then every reduced k-residue Jk(n)/Jk(d) pairwise disjoint reduced k-residue systems (mod d). 42. 4. 43. Let k. 44. k If f k = k1 + ... + k t • be a positive integer and suppose that i = 1. For all t. n. is a multiplicative function and i f f 1, f fT , then is completely multiplicative.

F(d)G(n/d) L din din Let k be a positive integer. is the convolution of only if f-l(pa) = 0 L 62. •. *gk. k n for all n. A multiplicativE function completely multiplicative functions if and for all primes gl" .. ,gk If g(d)F(n/d) p and all a > k + 1. l(n) gl (n) ... 63. If gl' g2' hI and h2 are completely multiplicative functions then where, for all n, if n is a square otherwise. 64. f then F 1. 65. 12 holds for a multiplicative function ~ pB. 66. A specially multiplicative function multiplicative i f and only i f 1.

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Elementary Number Theory (Series of Books in the Mathematical Sciences) by Underwood Dudley


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