- #1

physics kiddy

- 135

- 1

## Homework Statement

Let S

_{n}= n

^{2}+20n+12, n is a positive integer. What is the sum of all possible values of n for which S

_{n}is a perfect square ?

## Homework Equations

## The Attempt at a Solution

Well, I tried to factorise it : n

^{2}+20n+12 = n

^{2}+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 ?