Mersenne Numbers And Fermat Numbers Av Elena (Moscow State Pedagogical University Russia) Deza

<p>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.</p><p><br></p><p>In Mathematics, a Mersenne number (named after Marin Mersenne, who studied them in the early 17-th century) is a number of the form <em>M</em>_<em>n</em> = 2^<em>n</em> - 1 for positive integer <em>n</em>.</p><p><br></p><p>In Mathematics, a Fermat number (named after Pierre de Fermat who first studied them) is a positive integer of the form <em>F</em>_<em>n</em><em> = 2</em>^<em>k</em><em>+ 1</em>, <em>k=2</em>^<em>n</em>, where <em>n</em> is a non-negative integer.</p><p><br></p><p>Mersenne and Fermat numbers have many other interesting properties. Long and rich history, many arithmetic connections (with perfect numbers, with construction of regular