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A258928 a(n) = number of integral points on the elliptic curve y^2 = x^3 - (n^2)*x + 1, considering only nonnegative values of y. 0

%I

%S 3,6,11,9,15,13,14,17,26,12,12,11,12,19,20,11,19,36,12,17,16,11,19,16,

%T 15,27,17,17,18,16,12,15,17,11

%N a(n) = number of integral points on the elliptic curve y^2 = x^3 - (n^2)*x + 1, considering only nonnegative values of y.

%C For n>3, the number of integral points on y = x^3 - (n^2)*x + 1 is at least 11. These 11 points correspond to the solutions x = {-1, 0, n, -n, n + 2, -n + 2, n^2 - 1, n^2 - 2n + 2, n^2 + 2n + 2, n^4 + 2n, n^4 - 2n}.

%e a(0) = 3 because the integer points on y^2 = x^3 + 1 are (-1, 0), (0, 1), and (2, 3).

%Y Cf. A081119, A081120, A259191.

%K nonn,more

%O 0,1

%A _Morris Neene_, Jun 14 2015

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)