On The Diophantine Equation ∑x_i^2+a=y^2 And ∑x_i^3+a=y^3

Hari Kishan; Megha Rani; . Sarita

Hari Kishan Department of Mathematics, D.N. College, Meerut (U.P.) India
Megha Rani Department of Mathematics, RKGIT, Ghaziabad (U.P.) India
. Sarita Department of Mathematics, DCR University, Murthal, Sonipat (Haryana) India

Keywords: Diophantine equation and integral solution.

Abstract

In this paper, the Diophantine equations ∑𝒙_𝒊^𝟐+𝒂=𝒚^𝟐 and ∑𝒙_𝒊^𝟑+𝒂=𝒚^𝟑 where 𝑥₁≠𝑥₂≠𝑥₃≠⋯ and a is a positive integer have been discussed for possible positive integral solutions.

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