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%I #10 Apr 03 2014 05:41:55
%S 0,1,36
%N Triangular numbers that are squares of triangular numbers.
%C Ljunggren used p-adic methods to prove that 0, 1, and 36 are the only triangular numbers that are squares of triangular numbers.
%C Same as: the only positive integer solutions of (x(x-1))^2 = 2y(y-1) are (x,y) = (1,1), (2,2), and (4,9).
%C Cassels used elliptic curves to simplify Ljunggren's proof.
%C Subsequence of A001110 (triangular numbers that are squares).
%H W. Ljunggren, <a href="http://zbmath.org/scans/134/275.gif">Review of "Integral points on certain elliptic curves" by J.W.S. Cassels, Proc. Lond. Math. Soc., III. Ser. 14 A (1965), 55-57</a>, zbMATH 0134.27501.
%e 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2 = (1 + 2 + 3)^2.
%Y Cf. A000217, A001110.
%K nonn,fini,full,bref
%O 1,3
%A _Jonathan Sondow_, Apr 02 2014
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