Mersenne Numbers And Fermat Numbers

This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes. There is also extensive discussions of applied issues related to Cryptography.

In Mathematics, a Mersenne number (named after Marin Mersenne, who studied them in the early 17-th century) is a number of the form M_n = 2ⁿ - 1 for positive integer n.

In Mathematics, a Fermat number (named after Pierre de Fermat who first studied them) is a positive integer of the form F_n = 2^k+ 1, k=2ⁿ, where n is a non-negative integer.

Mersenne and Fermat numbers have many other interesting properties. Long and rich history, many arithmetic connections (with perfect numbers, with construction of regular