A094596 Number of solutions to the Lebesgue-Nagell equation x^2 + n = y^k with k > 2.

1, 0, 2, 0, 0, 7, 1, 0, 0, 2, 1, 1, 0, 3, 2, 1, 2, 2, 1, 0, 0, 3, 0, 1, 2, 1, 8, 0, 0, 3, 3, 0, 0, 1, 0, 0, 0, 4, 1, 0, 0, 0, 1, 2, 0, 5, 3, 2, 0, 0, 0, 3, 1, 3, 2, 0, 0, 0, 6, 1, 0, 5, 3, 1, 0, 1, 0, 0, 0, 4, 2, 0, 2, 0, 2, 1, 0, 2, 1, 2, 0, 2, 0, 0, 0, 3, 0, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0, 1, 4

Offset

2,3

Comments

Bugeaud, Mignotte and Siksek find all solutions for n <= 100.

Links

Table of n, a(n) for n=2..100.

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; Do[x=Sqrt[y^k-n]; If[IntegerQ[x], cnt++ ], {k, 3, 20}, {y, 600}]; cnt, {n, 2, 100}]

Crossrefs

Cf. A094597, A094598, A094599.

Sequence in context: A246608 A100344 A370796 * A143024 A271971 A278157

Adjacent sequences: A094593 A094594 A094595 * A094597 A094598 A094599

Keyword

hard,nonn

Author

T. D. Noe, May 13 2004

Status

approved