I suspect that this is a question for Max, assuming that he still looks in on the site ?
I watched a film on TV a couple of nights ago, it was called X + Y and was about a boy and a Maths Olympiad.
There wasn't much maths in the film but this was a question that did appear on screen.
Are there an infinite number of integer pairs (m, n) with the property that both
\(\displaystyle \frac {n^{2}+1}{m} \text{ and }\frac{m^{2}+1}{n}\)
are integers ?
I've fiddled around with it without really making any significant progress, a nudge in the right direction (but not a complete solution) would be good.
