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
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
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