I understand that for the first step, I just have to find an integer $t$ such that $0\leq t\leq 100$ such that $t^2-56$ is not a perfect square mod $101$. I know that to show that $t^2-56$ is not a perfect square mod $101$, I just have to show that $(t^2-56)^{50}-1$ is not divisible by $101$ (right?). I want to pick a $t$ and calculate. The problem is, is that once I plug in $t$, $(t^2-56)^{50}$ is too large for my calculator to handle. So how do I check that given a $t$, $(t^2-56)^{50}-1$ is not divisible by $101$?
(this is a homework question, and we are allowed to use any internet resources). So far, what we have done in class is prove that the group of units of a finite field is cyclic, and of course Fermat's Little Theorem.