A New Method in the Problem of Three Cubes
Number Theory
2018-02-21 v1
Abstract
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 P1(y)^3+P2(y)^3+P3(y)^3=Q(y). Actually, the solution of this problem has close relation with the problem of the sum of three cubes a^3+b^3+c^3=d, since deg Q(y)=0 case coincides with above mentioned problem. It has been considered estimation of possibility of minimization of deg Q(y). As a conclusion, for specific values of d we survey a new algorithm for finding integer solutions of a^3+b^3+c^3=d.
Keywords
Cite
@article{arxiv.1802.06776,
title = {A New Method in the Problem of Three Cubes},
author = {Armen Avagyan and Gurgen Dallakyan},
journal= {arXiv preprint arXiv:1802.06776},
year = {2018}
}