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2013 A quintic diophantine equation with applications to two diophantine systems concerning fifth powers
Ajai Choudhry, Jarosł aw Wróblewski
Rocky Mountain J. Math. 43(6): 1893-1899 (2013). DOI: 10.1216/RMJ-2013-43-6-1893

Abstract

In this paper we obtain a parametric solution of the quintic diophantine equation $ab(a+b)(a^2+ab+b^2)=cd(c+d)(c^2+cd+d^2)$. We use this solution to obtain parametric solutions of two diophantine systems concerning fifth powers, namely, the system of simultaneous equations $x_1+x_2+x_3 = y_1+y_2+y_3 =0$, $x_1^5+x_2^5+x_3^5 = y_1^5+y_2^5+y_3^5$, and the system of equations given by $\sum_{i=1}^5x_i^k =\sum_{i=1}^5 y_i^k$, $k=1,\,2,\,4,\,5$.

Citation

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Ajai Choudhry. Jarosł aw Wróblewski. "A quintic diophantine equation with applications to two diophantine systems concerning fifth powers." Rocky Mountain J. Math. 43 (6) 1893 - 1899, 2013. https://doi.org/10.1216/RMJ-2013-43-6-1893

Information

Published: 2013
First available in Project Euclid: 25 February 2014

zbMATH: 1345.11023
MathSciNet: MR3178448
Digital Object Identifier: 10.1216/RMJ-2013-43-6-1893

Subjects:
Primary: 11D41

Keywords: Equal sums of powers , Fifth powers , Quintic equation

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

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Vol.43 • No. 6 • 2013
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