I went insane trying to solve this problem (IMO 1988 Question 6)

My walkthrough of this famously difficult problem from the 1988 International Mathematics Olympiad.

Edit (4/10/2020) - I have realised this proof is actually incomplete. The general method is okay, but I missed a small detail. I needed to rearrange the formula in two ways, both in terms of x and also in terms of y. The important detail is to show that for the smaller "x" solution, there will also be two more solutions for y, then two further solutions for x, and so on... hence the infinite descent and contradiction. See my rewritten proof linked below

numberphile video: https://youtu.be/Y30VF3cSIYQ

Rewritten proof: http://bit.ly/3iTHM1e

Видео I went insane trying to solve this problem (IMO 1988 Question 6) канала Maths Explained