Look at the function $r_5(n)$, which is defined by the number of ordered integers $(a,b,c,d,e)$ which satisfy $a^2+b^2+c^2+d^2+e^2= n$. Now, I have conjectured that the unit's digit of $r_5(n)$ is 2 when $n$ is of the form $5p^2$, and its unit's digit is 0 when $n$ is not of that form. Is there any proof for my conjecture?
I have checked this for very large values of $p$ (upto $p= 100$). But can this be proved?