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A020896
Positive numbers k such that k = x^5 + y^5 has a solution in nonzero integers x, y.
2
2, 31, 33, 64, 211, 242, 244, 275, 486, 781, 992, 1023, 1025, 1056, 1267, 2048, 2101, 2882, 3093, 3124, 3126, 3157, 3368, 4149, 4651, 6250, 6752, 7533, 7744, 7775, 7777, 7808, 8019, 8800, 9031, 10901, 13682, 15552, 15783, 15961, 16564
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
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