Relation and proving reflexivity

Question

The relation R is defined on integers by $xRy$ if and only if $x^2y=ymod6$. Prove that $R$ is reflexive.

So far I have:

Let $x=y$

$x^2x=xmod6$

I don't know how to go from here... because $x^2=0mod6$ is not true...

Answer 1

Hint: We have

$$x^3-x=x(x-1)(x+1)$$ so for three consecutive numbers certainly there is one multiple of $2$ and another multiple of $3$.