A New Method in the Problem of Three Cubes

In the current paper we are seeking P1(y), P2(y), P3(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, such that P 3 1 (y)+P 3 2 (y)+P 3 3 (y) = Q(y). Actually, the solution of this problem has close relation with the problem of the sum of three cubes a + b + c = d, since degQ(y) = 0 case coincides with above mentioned problem. It has been considered estimation of possibility of minimization of degQ(y). As a conclusion, for specific values of d we survey a new algorithm for finding integer solutions of a + b + c = d.