Sum of Three Biquadatics a Multiple of a n th Power, n = (2,3,4,5,6,7,8 & 9)

Abstract

Consider the below mentioned equation: x4+y4+z4=w∗tn----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x4+y4+z4=w∗tn--- (A)