Determine general solution to problem to find more square


Given the whole number N which is not the square, how do we find the square such that when we multiply N and add 1, result is also a square?

For instance N=7, 9N+1=64
9 is 3^2 and 64 is 8^2.

Determine the general solution to problem to find more squares?
Determine the solution for N=61 be?
Determine  this (sum square)61+1=(Another square)

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Mathematics: Determine general solution to problem to find more square
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