Factors and Equations

$N + 74 = x^2$ (1)

$N - 15 = y^2$ (2)

Subtracting (2) from (1) gives

$89 = x^2 - y^2$ which can be factored to give $89 = (x-y)(x+y)$

After some close inspection you will find $89$ is a prime number. Therefore the only factors of $89 = 89 * 1$

Since $x + y > x - y$ we therefor have

$x + y = 89$ and

$x - y = 1$

adding these gets $2x = 90$ , thus $x=45$ thus $45^2 - 74 = 1951$