Show that there are no intergers $x$ and $y$ such that
Hint from professor:
Consider the equation in a convenient $\mod (n)$ so that you end up with a polynomial in a single variable. Then proceed as solving number of congruence.
Im not sure how to approach this question
then $x^2-5y^2=0$ $\to$ $x^2=5y^2$
we have $5y^2\equiv0\mod(x)$
then how do I continue..?