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 A240129 Triangular numbers that are squares of triangular numbers. 1
 0, 1, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Ljunggren used p-adic methods to prove that 0, 1, and 36 are the only triangular numbers that are squares of triangular numbers. 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). Cassels used elliptic curves to simplify Ljunggren's proof. Subsequence of A001110 (triangular numbers that are squares). LINKS W. Ljunggren, Review of "Integral points on certain elliptic curves" by J.W.S. Cassels, Proc. Lond. Math. Soc., III. Ser. 14 A (1965), 55-57, zbMATH 0134.27501. EXAMPLE 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2 = (1 + 2 + 3)^2. CROSSREFS Cf. A000217, A001110. Sequence in context: A107736 A261121 A139474 * A023929 A010113 A167264 Adjacent sequences:  A240126 A240127 A240128 * A240130 A240131 A240132 KEYWORD nonn,fini,full,bref AUTHOR Jonathan Sondow, Apr 02 2014 STATUS approved

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Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)