Factors of generalized Fermat numbers

Dubner, Harvey; Keller, Wilfrid

doi:10.1090/S0025-5718-1995-1270618-1

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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