Subject: Calculus Problem Hi my name is William and I'm a 12th grade student pondered by a problem my calculus teacher gave me. Find all pair of positive integers m and n such that mn + m + n divides m^{2} + n^{2} = 1. Please I would appreciate any type of help William Hi Willaim,If (mn + m + n)/(m^{2} + n^{2}) = 1 then mn + m + n = m^{2} + n^{2}. Rearrange the terms to write this expression as a quadratic in m, that is If you use the general quadratic to solve for m, and m is to be an integer, then the discriminant (the piece under the root sign) must be a square. That is must be a square. Simplified this expression is Notic that when n is large this expression is negative and hence can't be a square. Since n is a positive integer substitute n = 1, 2, 3,... until the expression is negative. For each positive value that is a square substitute the value of n into the original expression and solve for m. Cheers,Penny
