## Rocky Mountain Journal of Mathematics

### A quintic diophantine equation with applications to two diophantine systems concerning fifth powers

#### 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 $\sum_{i=1}^5x_i^k =\sum_{i=1}^5 y_i^k$, $k=1,\,2,\,4,\,5$.

#### Article information

Source
Rocky Mountain J. Math., Volume 43, Number 6 (2013), 1893-1899.

Dates
First available in Project Euclid: 25 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1393336661

Digital Object Identifier
doi:10.1216/RMJ-2013-43-6-1893

Mathematical Reviews number (MathSciNet)
MR3178448

Zentralblatt MATH identifier
1345.11023

Subjects
Primary: 11D41: Higher degree equations; Fermat's equation

#### Citation

Choudhry, Ajai; Wróblewski, Jarosł aw. A quintic diophantine equation with applications to two diophantine systems concerning fifth powers. Rocky Mountain J. Math. 43 (2013), no. 6, 1893--1899. doi:10.1216/RMJ-2013-43-6-1893. https://projecteuclid.org/euclid.rmjm/1393336661

#### References

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