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Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 5(3), pp. 45 - 56
DOI: 10.13189/ujcmj.2017.050301
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A New Method in the Problem of Three Cubes

Armen Avagyan ^*, Gurgen Dallakyan
Armenian State Pedagogical University after Khachatur Abovyan, Armenia

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 = Q(y). Actually, the solution of this problem has close relation with the problem of the sum of three cubes a³ + b³ + c³ = 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 a³ + b³ + c³ = d.

KEYWORDS
Diophantine Equation, Sum of Three Cubes, Parametic Solutions

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Armen Avagyan , Gurgen Dallakyan , "A New Method in the Problem of Three Cubes," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 5, No. 3, pp. 45 - 56, 2017. DOI: 10.13189/ujcmj.2017.050301.

(b). APA Format:
Armen Avagyan , Gurgen Dallakyan (2017). A New Method in the Problem of Three Cubes. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 5(3), 45 - 56. DOI: 10.13189/ujcmj.2017.050301.