1988 Putnam B6

Prove that there exist an infinite number of ordered pairs $(a,b)$ of

integers such that for every positive integer $t$, the number $at+b$

is a triangular number if and only if $t$ is a triangular number. (The

triangular numbers are the $t_n = n(n+1)/2$ with $n$ in $\{0,1,2,\dots\}$.)

证明存在无限多个有序对 $(a,b)$

整数，使得对于每个正整数 $t$，数字 $at+b$

是一个三角数当且仅当 $t$ 是一个三角数。 (

三角数是 $t_n = n(n+1)/2$，其中 $n$ 位于 $\{0,1,2,\dots\}$ 中。)