Elliptic binomial diophantine equations

The complete sets of solutions of the equation ((n)(k)) = ((m)(l)) are dete rmined for the cases (k, l) = (2, 3), (2, 4), (2, 6), (2, 8), (3, 4), (3, 6 ), (4, 6), (4, 8). In each of these cases the equation is reduced to an ell iptic equation, which is solved by using linear forms in elliptic logarithm s. In all but one case this is more or less routine, but in the remaining c ase ((k, l) = (3, 6)) we had to devise a ne iv variant of the method.