
COMMENTS

Bennett proved that if a, b, c are nonzero integers with a > 1 and b > 1, then the equation a^x  b^y = c has at most two solutions in positive integers x and y.
Bennett conjectured that if a, b, c are positive integers with a > 1 and b > 1, then the equation a^x  b^y = c has at most one solution in positive integers x and y, except for the triples (a,b,c) = (3,2,1), (2,5,3), (6,2,4), (2,3,5), (15,6,9), (13,3,10), (2,3,13), (91,2,89), (280,5,275), (6,3,1215), (4930,30,4900). If this is true, then the present sequence is complete.
