Number Theory

I'm not clear on what the problem states, but I'm assuming it means that 0,1,2,3,4 are plugged in as x. 

So, see...

What the equation is saying is that x^5 must be divisble by 5. 

Let's plug in numbers

$0^5 \equiv 0 \pmod{5}$ so it works

$1^5 = 1 \equiv 1 \pmod5$ so it doesn't work

$2^5 = 32 \equiv 2 \pmod5$ so it doesn't work

$3^5=243\equiv3 \pmod 5$ so it doesn't work

$4^5 = 1024 \equiv 4 \pmod 5$ so it doesn't work

So the only one that works is 0. 

Then again, residue is usually used as the remainder, but I hope my asusmption is correct.

Thanks! :)