OFFSET
0,1
COMMENTS
68101 = (15/2)^5 + (17/2)^5 is believed to be the smallest positive integer k which is the sum of two nonzero fifth powers of rational numbers but not the sum of two nonzero fifth powers of integers.
REFERENCES
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Steven R. Finch, On a Generalized Fermat-Wiles Equation [broken link]
Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]
FORMULA
See Theorem 3.5.6 of J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99.
EXAMPLE
31 = 2^5 + (-1)^5.
MATHEMATICA
Select[Union[Total/@(Select[Tuples[Range[-8, 8], {2}], !MemberQ[#, 0]&]^5)], #>0&] (* Harvey P. Dale, Apr 03 2011 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
STATUS
approved