ON THE EQUATION A(3)+B(3)-C(P)

Let p be a prime number greater than or equal to 17. This paper deals with the diophantine equation a(3) + b(3) = c(p). If we suppose that t he Taniyama-Weil conjecture is true, we get a criterion that often all ows one to prove that this equation has no nonzero integer solution wi th a, b and c coprime. In particular, we verify that this is the case if p is < 10000.