eBook - ePub

Number Theory

Name: Number Theory
ISBN: 9783111579542

Multiplicative and Additive with Factorization and Primality Testing

Peter D. Schumer,

English
ePUB (mobile friendly)
Available on iOS & Android

eBook - ePub

Number Theory

Multiplicative and Additive with Factorization and Primality Testing

Peter D. Schumer,

About this book

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.

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Yes, you can access Number Theory by Peter D. Schumer in PDF and/or ePUB format, as well as other popular books in Mathematics & Computer Science General. We have over one million books available in our catalogue for you to explore.