On the simultaneous Diophantine equations m.(x₁^k+....+x_t1^k)=n.(y₁^k+....+y_t2^k); k=1,3

2017/05/03 by Farzali Izadi, Izadi, Farzali, Mehdi Baghalaghdam +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory #Chaos-based Image/Signal Encryption #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1705.01381

openalex publication_date 2017/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we solve the simultaneous Diophantine equations m.(x₁^k+....+x_t1^k)=n.(y₁^k+....+y_t2^k); k=1,3, where t₁, t₂>3, and m, n are fixed arbitrary and relatively prime positive integers. This is done by choosing two appropriate trivial parametric solutions and obtaining infinitely many nontrivial parametric solutions. Also we work out some examples, in particular the Diophantine systems of A^k+B^k+C^k=D^k+E⁴; k=1,3.

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