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. 

Although equation:
$(n+20)+(n+21)+...+(n+100)=81(n+60)=81y^2$
Solutions have the form:
$y=\frac{k+1}{2}$
$n=\frac{k^2+2k-239}{4}$
$k$ - can be any character.
