Proof question of integers. Let $a$ and $b$ be positive integers such that $ab+1$ divides $a^2+b^2$.  Show that $\frac{a^2+b^2}{ab+1}$ is the square of an integer.
Numberphile did a detailed 2 part video on the question:
Part 1: https://www.youtube.com/watch?v=Y30VF3cSIYQ
Part 2: https://www.youtube.com/watch?v=L0Vj_7Y2-xY
Numberphile did a detailed 2 part video on the question:
Part 1: https://www.youtube.com/watch?v=Y30VF3cSIYQ
Part 2: https://www.youtube.com/watch?v=L0Vj_7Y2-xY