The diophantine equation x3 _ 3xy2 _y3 = ?3no 17 n l9n2 is completely solved as follows. First, a large upper bound for the variables is obtained from the theory of linear forms in p-adic and real logarithms of algebraic numbers. Then this bound is reduced to a manageable size by p-adic and real computational diophantine approximation, based on the L3-algorithm. Finally the complete list of sol...
