2023/04/09 by Ajai Choudhry, Choudhry, Ajai
Mathematics · Physics and Astronomy · #History and Theory of Mathematics #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2305.07657
In this paper we present a new method of solving the classical diophantine equation A4+B4=C4+D4. Two methods of solving this equation, given by Euler, yield parametric solutions given by polynomials of degrees 7 and 13. Several other parametric solutions are now known, and with the exception of one solution of degree 11, all the published solutions are of degrees 6n+1 for some integer n. The method described in this paper yields new parametric solutions of degrees 21, 39 and 75, that is, degrees that are expressible as 6n+3.