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
EXAMPLE
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2 = (1 + 2 + 3)^2.
CROSSREFS
KEYWORD
nonn,fini,full,bref
AUTHOR
Jonathan Sondow, Apr 02 2014
STATUS
approved