A square integer N ends in 4 identical digits d in its decimal representation, where . Find all possible values of d. For each admissable value of d, find a possible N.

N is a perfect square whose second-to-last digit is odd. What can its last digit be?

Find all positive integers (x, y) for which .

Solve for , where x and y are positive integers.

Prove that the congruence , has exactly 4 solutions modulo .