Find all values of n such that n^2-13n+50 is a perfect square

Answer 1

looks intereseting. lets see:

since a polynomial is defined by at least three points, if there were 3 or more perfect square values, there would be an infinite number of perfect square values, because the polynomial would be factorable into a perfect square. since this polynomial is not factorable into a perfect square, there can be at most two values where it can pass through a perfect square point.

Excel says that the value 14 is at least one of these values. I leave you to check for the other and determine how to find this value manually