Is it possible to find all integers m>0 and n>0 such that n+1∣m2+1 and m+1|n2+1 ?
I succeed to prove there is an infinite number of solutions, but I cannot progress anymore.
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.