abstract: If we factor x2+x = 2a 3b y, with a, b, x and y nonnegative integers, then it has been known for almost 700 years that y > 1 provided x > 8. We will show how to derive a lower bound of the shape y > x(14), valid for all x > 8 and sketch (curious) connections between this result and the Inverse Galois Problem. This is joint work with Michael Filaseta and Ognian Trifonov.