Sum of Three Biquadatics a Multiple of a nth Power, n =(2,3,4,5,6,7,8, 9)
Author(s) -
Seiji Tomita,
Oliver Couto
Publication year - 2016
Publication title -
universal journal of applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2331-6446
pISSN - 2331-6470
DOI - 10.13189/ujam.2016.040103
Subject(s) - mathematics , combinatorics , power (physics) , discrete mathematics , physics , quantum mechanics
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)
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