On the simultaneous Diophantine equations $$ m \cdot (x_1^k+x_2^k+ \cdots + x_{t_1}^k)=n \cdot (y_1^k+y_2^k+ \cdots y_{t_2}^k)$$ m · ( x 1 k + x 2 k + ⋯ + x t 1 k ) = n · ( y 1 k + y 2 k + ⋯ y t 2 k ) ; $$k=1,3$$ k = 1 , 3

Autor: Farzali Izadi, Mehdi Baghalaghdam
Rok vydání: 2017
Předmět:
Zdroj: Periodica Mathematica Hungarica. 75:190-195
ISSN: 1588-2829
0031-5303
DOI: 10.1007/s10998-017-0183-2
Popis: In this paper, we solve the simultaneous Diophantine equations $$m \cdot ( x_{1}^k+ x_{2}^k +\cdots + x_{t_1}^k)=n \cdot (y_{1}^k+ y_{2}^k +\cdots + y_{t_2}^k )$$ , $$k=1,3$$ , where $$ t_1, t_2\ge 3$$ , 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 $$A^k+B^k+C^k=D^k+E^k$$ , $$k=1,3$$ .
Databáze: OpenAIRE
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