Problem - 173
For any arithmetic sequence whose terms are all positive integers, show that if one term is a perfect square, this sequence must have infinite number of terms which are perfect squares.
Let $d$ be the common difference and the perfect square term be $m^2$, where both $d$ and $m$ are positive integer. Let $k$ be any positive integer, then the term $m^2+(2km + dk^2)d = (m+kd)^2$ is also a perfect square.