**For a prime $p$, if $x^p \equiv y^p \pmod p $**

**Then prove that;
$x^p \equiv y^p(\bmod p^2) $**

Firstly I am confused where to approach to prove this question ,though i know several propositions and theorems related to congruences 

Like by applying fermat's theorem we can easily derive 
$x\equiv y \pmod p $
But what to do after that ?

Secondly i approached with the proposition that ,iff
$x \equiv y (\bmod n\_i)$ And for $i=1,2$
Then 
$x \equiv y (\bmod [n\_1,n\_2]) $

But i am unable to prove the question with these two approaches 

Please tell whether either of my approaches will help to prove the question if not then please give a proper proof with steps for the same 

This is an olympiad book question(not a homework problem)