Here’re the problems:

- 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 .

That’s all. 🙂