The diophantine equation x⁴+y⁴=z⁴+w⁴

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.