IMO 1969 - Longlist Problems Question 17

(CZS 6) Let $d$ and $p$ be two real numbers. Find the first term of an arithmetic progression $a_1,a_2,a_3,\ldots$ with difference $d$ such that $a_1a_2a_3a_4=p$. Find the number of solutions in terms of $d$ and $p$.