Calculate the last two decimal places of $\displaystyle 3^{57} $. I have no idea how to do this question.

and

Find the integers x and y that solve each of the following equations, or explain why no solution exists

(a) $\displaystyle 1856x + 984y = 4 $

(b) $\displaystyle 11111111x + 3333y = 4444 $

(c) $\displaystyle 968x + 372y = 4 $

(remembering this is in a number theory context)