Question

Compute the remainder modulo 7 of $\displaystyle 2222^5555$

My notes do not make this explicit so I ask here. Is this question asking for a number x such that $\displaystyle x\equiv{2222^{5555}} (mod{ }n)$

If so, then this question is equivalent to solving the diophantine equation

$\displaystyle x-7k=2222^{55555}$

?

And I need to find the least positive integer x that satisfies this equation?

How shall I proceed to do this?