a and b are positive integers. Dividing a² + b² by a + b we obtain the quotient as q and the remainder as r.

Determine analytically all possible pairs (a, b) such that q² + r = 2547

I have made the assumption that r is the numerator of the remainder of the division result, ie. the proper fraction of the mixed number [Q  r/(a+b) ].  For if r were the remainder, in order for the equation, q2 + r, to equal a whole number, as is 2547, r would need be zero.

Two of the pairs are (24, 61) and, of course, (61, 24).

Edited on March 30, 2007, 10:15 am

Posted by Dej Mar on 2007-03-30 00:54:54