The Legend of Six

1. Problem Statment

Consider the following problem: Let a and b be positive integers such that $ab + 1$ divides $a^2 + b^2$. Show that below

\[\frac{a^2 + b^2}{1 + ab}\]

is the square of an integer.

This was the sixth problem in IMO, 1988 head at Canberra. You can find some lores around this in the references

2. Approach

References

1. IMO 1988 Question 6
2. Some lores about it
3. Solution on Numberphile