Inspired From Satvik Golechha

Number Theory Level 5

\[ n^2+25n+7=m^2\]

Consider all ordered pairs of integers \((m,n) \) such that the above equation is fulfilled.

Let the sum of all integral values of \(m \) and \(n\) to be \(a \) and \(b\) respectively. What is the value of \(a-b\)?

Image Credit: Wikimedia Square Root

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