Just a quick break

$(x + y)(x-y) = 31$ and $31$ is a prime number, so $x + y = 31$ and $x-y = 1$ , which means that $x = 16$ and $y = 15$ . And then it's simple.

$n^{2} +2n+1=(n+1)^{2}$ $2n+1=31 , n= 15, n+1=16$ if in a math similar to this, $(n+1)^{2}$ doesn 't work, use $n^{2}+4n+4=(n+2)^{2}$ and so on......