The Problem:
Suppose for a positive integer n both 5n+1 and 7n+1 are perfect squares. Show that n is divisible by 24

My attempt:
Since 5n+1 is a perfect square and n is a positive integer then, the n's for which 5n+1 is a perfect square are: n= 3, 7, 16, 24 ..........
and for 7n+1 : n = 5, 9, 24......
therefore the least common 'n' which makes both 5n+1 and 7n+1 a perfect square is 24 and therefore 'n' is divisible by 24.

Any better approach to this problem?