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Since 1772, when Euler first described two methods of obtaining two pairs of biquadrates with equal sums, several methods of solving the diophantine equation x⁴+y⁴=z⁴+w⁴ 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.
Choudhry et al. (Sun,) studied this question.