Question 73
Consider a non-constant arithmetic progression $a_1, a_2, \dots, a_n, \dots$. Suppose there exist relatively prime positive integers $p \gt 1$ and $q \gt 1$ such that $a_1^2, a_{p+1}^2$ and $a_{q+1}^2$ are also the terms of the same arithmetic progression. Prove that the terms of the arithmetic progression are all integers.