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A094597
Number of solutions to the Lebesgue-Nagell equation x^2 + n = y^k with k > 2 and unique x.
3
1, 0, 2, 0, 0, 5, 1, 0, 0, 2, 1, 1, 0, 2, 2, 1, 2, 2, 1, 0, 0, 3, 0, 1, 2, 1, 6, 0, 0, 2, 3, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 0, 1, 2, 0, 5, 2, 2, 0, 0, 0, 2, 1, 2, 2, 0, 0, 0, 4, 1, 0, 3, 2, 1, 0, 1, 0, 0, 0, 3, 2, 0, 2, 0, 2, 1, 0, 2, 1, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0, 1, 4
OFFSET
2,3
COMMENTS
Solutions such as 181^2+7 = 32^2 = 8^5 = 2^15 are counted only once. A094596 counts this as three solutions. Bugeaud, Mignotte and Siksek find all solutions for n <= 100.
EXAMPLE
a(4) = 2 because there are two solutions: 2^2+4=2^3 and 11^2+4=5^3.
MATHEMATICA
Table[cnt=0; xLst={}; Do[x=Sqrt[y^k-n]; If[IntegerQ[x] && !MemberQ[xLst, x], cnt++; AppendTo[xLst, x]], {k, 3, 20}, {y, 600}]; cnt, {n, 2, 100}]
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, May 13 2004
STATUS
approved