Factors of Generalized Fermat Numbers

Abstract

Generalized Fermât numbers have the form Fb<m = b1" +1 .Their odd prime factors are of the form k • 2" + 1, k odd, n > m.It is shown that each prime is a factor of some F¡, m for approximately 1 /k bases b , independent of n .Divisors of generalized Fermât numbers of base 6, base 10, and base 12 are tabulated.Three new factors of standard Fermât numbers are included.