1. The problem statement, all variables and given/known data Let Sn = n2+20n+12, n is a positive integer. What is the sum of all possible values of n for which Sn is a perfect square ? 2. Relevant equations 3. The attempt at a solution Well, I tried to factorise it : n2+20n+12 = n2+20n+100-88 =(n+10)2-88. And I conclude that there are infinitely such values of n... I also tried to search properties of perfect squares but could find none applicable here. To my surprise, answer is 16 .... How is it like that ???