CONJECTURE (GENERAL FERMAT NUMBERS) Florentin Smarandache, Ph D Associate Professor Chair of Department of Math & Sciences University of New Mexico 200 College Road Gallup, NM 87301, USA E-mail: [email protected] Let’s consider a, b integers 2 and k an integer such that a, c 1. One constructs the function P(k) abk c, where k 0,1,2,... . Then: a) For any given triplet a, b, c there is at least k such that P(k ) is 0 0 prime. b) There doesn’t exist a triplet a, b, c such that P(k) is prime for all k 0. c) Is it possible to find a triplet a, b, c such that P(k) is prime for infinitely many k’s?