id:A094597 - OEIS Search Results

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Number of solutions to the Lebesgue-Nagell equation x^2 + n = y^k with k > 2 and unique x.

+0
4

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 (list; graph; listen)

	OFFSET	`2,3`
	COMMENT	`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.`
	LINKS	`Yann Bugeaud, Maurice Mignotte and Samir Siksek, Classical and modular approaches to exponential Diophantine equations II. The Lebesgue-Nagell equation`
	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	`Cf. A094596, A094598, A094599.` `Sequence in context: A048243 A057611 A147843 this_sequence A143160 A095221 A078112` `Adjacent sequences: A094594 A094595 A094596 this_sequence A094598 A094599 A094600`
	KEYWORD	`hard,nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), May 13 2004`

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Last modified November 30 22:12 EST 2008. Contains 150989 sequences.

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