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arXiv · 1802.06776

A New Method in the Problem of Three Cubes

Armen Avagyan·Gurgen Dallakyan
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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.

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Armen Avagyan, Gurgen Dallakyan. 2018-02-18. A New Method in the Problem of Three Cubes. https://doi.org/10.13189/ujcmj.2017.050301

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