How many solutions (m,n positive integers only) are there for
(In reply to m, n < 50
by Steve Herman)
For every n between 1 and 49, there are up to 6 m between 1 and 49 that satisfy the equation.
49 * 6 = 294
But this overcounts, because for n between 1 and 12, there are only 5 positive m that work (1,2,3,4,5).
Total solutions = 294 - 12 = 282, which has the advantage of agreeing with Ady's spoiler.