I can find three pairs that work:
(A, B) = (4, 4), (5, 6) and (6, 5),
but I can't yet prove that no others exist.
They must lie in the 1st quadrant of the A-B plane 'outside' the parabolas a^2 = 4b and b^2 = 4a and there's plenty of room to explore there...
Posted by Harry
on 2016-10-19 17:15:01