Factors of generalized Fermat numbers

Authors:
Harvey Dubner and Wilfrid Keller

Journal:
Math. Comp. **64** (1995), 397-405

MSC:
Primary 11A51; Secondary 11Y05

DOI:
https://doi.org/10.1090/S0025-5718-1995-1270618-1

MathSciNet review:
1270618

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Abstract: Generalized Fermat numbers have the form ${F_{b,m}} = {b^{{2^m}}} + 1$. Their odd prime factors are of the form $k \cdot {2^n} + 1$, *k* odd, $n > m$. It is shown that each prime is a factor of some ${F_{b,m}}$ for approximately $1/k$ bases *b*, independent of *n*. Divisors of generalized Fermat numbers of base 6, base 10, and base 12 are tabulated. Three new factors of standard Fermat numbers are included.

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Article copyright:
© Copyright 1995
American Mathematical Society