Q:

Number theory with positive integer $n$ question

If $n$ is a positive integer, what is the smallest value of $n$ such that $$(n+20)+(n+21)+(n+22)+ ... + (n+100)$$ is a perfect square?
I don't even now how to start answering this question. 

A:

Write it as $81n+\frac{81}{2}(100+20)=81(n+60)$
$81$ is a perfect square. For what least $n$ is $60+n$ a perfect square?

$n=4$

