Questions tagged [triangular-numbers]

Numbers of the form 1+2+3+4+...+n

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If $T_n$ is the $n$-th triangular number, there are an infinite number of $a, b, c, d$ such that $T_n+T_{an+b} =(cn+d)^2 $ for all $n$.

If $T_n$ is the $n$-th triangular number, show that there are an infinite number of positive integers $a, b, c, d$ such that $T_n+T_{an+b} =(cn+d)^2 $ for all $n$. This is inspired by an article in ...