/sci/ - Science & Math

I'm new to 4chan but I am a professional mathematician. I'm curious to know, are there good mathematicians on this forum who will be able to discuss high level problems, or just college level mathtrolls? Can anyone prove themselves to me by solving this problem:

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There are some pairs of integers (n,m) such that both n divides m^2+1 and m divides n^2+1.

The pair (1,2) is an obvious example since 2 divides 1^2+1 = 2, and clearly 1 divides 2^2+1 = 5.

Prove that there are infinitely many such pairs.