Can you solve this? Question 7. Questions my students have asked.

Continuing my series on the interesting questions my students have asked me, in this article we look at a problem from the 1997 Polish Mathematical Olympiad. We will look at two ways to solve this problem and discuss a very useful general technique for solving problems of this form.

If you are interested, you can find all questions from this series, along with a discussion on my inspiration for the series, here.

The question from the Olympiad paper reads as follows:
Find all integer solutions…