2024 The diophantine equation $x^4+y^4=z^4+w^4$
Ajai Choudhry, Arman Shamsi Zargar
Funct. Approx. Comment. Math. Advance Publication 1-8 (2024). DOI: 10.7169/facm/240530-10-7

Abstract

Since 1772, when Euler first described two methods of obtaining two pairs of biquadrates with equal sums, several methods of solving the diophantine equation $x^4+y^4=z^4+w^4$ have been published. All these methods yield parametric solutions in terms of homogeneous bivariate polynomials of odd degrees. In this paper we describe a method that yields three parametric solutions of the aforesaid diophantine equation in terms of homogeneous bivariate polynomials of even degrees, namely degrees $74$, $88$ and $132$ respectively.

Citation

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Ajai Choudhry. Arman Shamsi Zargar. "The diophantine equation $x^4+y^4=z^4+w^4$." Funct. Approx. Comment. Math. Advance Publication 1 - 8, 2024. https://doi.org/10.7169/facm/240530-10-7

Information

Published: 2024
First available in Project Euclid: 16 December 2024

Digital Object Identifier: 10.7169/facm/240530-10-7

Subjects:
Primary: 11D25

Keywords: biquadrates , equal sums of biquadrates , fourth powers

Rights: Copyright © 2024 Adam Mickiewicz University

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