OFFSET
0,1
COMMENTS
It can be shown that, like the Fermat numbers, two of these generalized Fermat numbers are coprime if they have the same base k. However, unlike the Fermat numbers (which are conjectured to be squarefree), these generalized Fermat numbers are not necessarily squarefree for k > 1. Riesel tabulates some prime factors of generalized Fermat numbers for k <= 5.
REFERENCES
H. Riesel, "Prime numbers and computer methods for factorization," Second Edition, Progress in Mathematics, Vol. 126, Birkhauser, Boston, 1994, pp. 417-425.
LINKS
T. D. Noe, Factorizations of Generalized Fermat Numbers
Eric Weisstein's World of Mathematics, Generalized Fermat Number
MATHEMATICA
mx=5000; maxK=Ceiling[Sqrt[mx/2]]; maxM=Ceiling[Log[2, Log[2, mx]]]; lst={}; Do[gf=(k+1)^2^m+k^2^m; If[gf<mx, AppendTo[lst, gf]], {k, maxK}, {m, 1, maxM}]; lst1=Union[lst]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
T. D. Noe, Dec 12 2002
STATUS
approved