Peter D. Schumer
Number Theory: Multiplicative and Additive with Factorization and Primality Testing - De Gruyter Textbook Peter D. Schumer

Name: Number Theory: Multiplicative and Additive with Factorization and Primality Testing - De Gruyter Textbook
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Author: Peter D. Schumer

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Number Theory: Multiplicative and Additive with Factorization and Primality Testing - De Gruyter Textbook

Peter D. Schumer

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.

Media	Bøker Pocketbok (Bok med mykt omslag og limt rygg)
Utgitt	18. august 2025
ISBN13	9783111578675
Utgivere	De Gruyter
Antall sider	352
Mål	150 × 220 × 10 mm · 580 g