Question

Find the sum of the values of x and y for all the positive integer solutions for the equation:
\(\Large x^2-y^2=211\)

Answer 1

\(211\) is a prime number. So, it's only divisible by \(1\) and itself. Now, \((x + y)(x - y) = 211\) or, \(\large x + y = \frac{211}{(x - y)}\)
Since \(x\) and \(y\) both are positive integer the sum also can't be fraction and the chance of \(x - y\) being \(211\) is also emitted.
So \(x - y\) is \(1\). Then, \(x + y = 211\)