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...

blackjack

flooble's webmaster puzzle