How to solve these two simultaneous “divisibilities” : n+1∣m2+1n+1\mid m^2+1 and m+1∣n2+1m+1\mid n^2+1

Is it possible to find all integers m>0 and n>0 such that n+1m2+1 and m+1|n2+1 ?

I succeed to prove there is an infinite number of solutions, but I cannot progress anymore.

Thanks !


Some further results along the lines of thought of @individ:

Suppose p and s are solutions to the Pell’s equation:
are solutions if (a,b,c,d) are: (these are the only sets that I found using the computer)
Sadly, the solutions are negative.

Here are some examples:
P.S. I am also very curious how @individ thought of this parametrization.

Source : Link , Question Author : uvdose , Answer Author : Yifan Zhu

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