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 . Their odd prime factors are of the form , *k* odd, . It is shown that each prime is a factor of some for approximately 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.

**[1]**J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman, and S. S. Wagstaff, Jr.,*Factorizations of**up to high powers*, 2nd ed., Contemp. Math., vol. 22, Amer. Math. Soc., Providence, RI, 1988. MR**996414 (90d:11009)****[2]**C. Caldwell,*Review of the Cruncher PC plug-in board*, J. Recreational Math.**25**(1993), 56-57.**[3]**H. Dubner,*Generalized Fermat primes*, J. Recreational Math.**18**(1985-86), 279-280.**[4]**H. Griffin,*Elementary theory of numbers*, McGraw-Hill, New York, 1954. MR**0064063 (16:220d)****[5]**W. Keller,*Table of primes of the form*,*k*odd , Hamburg, 1993 (unpublished).**[6]**-,*Factors of Fermat numbers and large primes of the form*, Math. Comp.**41**(1983), 661-673; II (Preprint 27 September 1992). MR**717710 (85b:11117)****[7]**M. Morimoto,*On prime numbers of Fermat type*, Sûgaku**38**(1986), 350-354. (Japanese)**[8]**H. Riesel,*Common prime factors of the numbers*, BIT**9**(1969), 264-269. MR**0258735 (41:3381)****[9]**-,*Some factors of the numbers**and*, Math. Comp.**23**(1969), 413-415.

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

Article copyright:
© Copyright 1995
American Mathematical Society