Number Theory: Multiplicative and Additive with Factorization and Primality Testing - De Gruyter Textbook - Peter D. Schumer - Livros - De Gruyter - 9783111578675 - 18 de agosto de 2025
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Peter D. Schumer
Number Theory: Multiplicative and Additive with Factorization and Primality Testing - De Gruyter Textbook

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This is a book for an undergraduate number theory course, senior thesis work, graduate level study, or for those wishing to learn about applications of number theory to data encryption and security. With no abstract algebra background required, it covers congruences, the Euclidean algorithm, linear Diophantine equations, the Chinese Remainder Theorem, Mobius inversion formula, Pythagorean triplets, perfect numbers and amicable pairs, Law of Quadratic Reciprocity, theorems on sums of squares, Farey fractions, periodic continued fractions, best rational approximations, and Pell’s equation. Results are applied to factoring and primality testing including those for Mersenne and Fermat primes, probabilistic primality tests, Pollard’s rho and p-1 factorization algorithms, and others.

Also an introduction to cryptology with a full discussion of the RSA algorithm, discrete logarithms, and digital signatures. Chapters on analytic number theory including the Riemann zeta function, average orders of the lattice and divisor functions, Chebyshev’s theorems, and Bertrand’s Postulate. A chapter introduces additive number theory with discussion of Waring’s Problem, the pentagonal number theorem for partitions, and Schnirelmann density.

Mídia Livros     Paperback Book   (Livro de capa flexível e brochura)
Lançado 18 de agosto de 2025
ISBN13 9783111578675
Editoras De Gruyter
Páginas 352
Dimensões 150 × 220 × 10 mm   ·   580 g

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