How to prove that there is no infinite arithmetic progression of perfect squares
This question from a school Olympiad paper !
How can I prove this directly or using contradiction ?
For example : 1 ,25 , 49 are perfect squares and has 24 as the differnce ! but not infinite !
When $n^2 + d = m^2$ you get $(n-m)(n+m) = d$. For any fixed $d$ this limits the possible distinct values of $n,m$ to a finite collection. From this the claim follows quite directly.