Journals Information
Universal Journal of Applied Mathematics Vol. 4(1), pp. 22 - 31
DOI: 10.13189/ujam.2016.040103
Reprint (PDF) (189Kb)
Sum of Three Biquadatics a Multiple of a nth Power, n = (2,3,4,5,6,7,8 & 9)
Seiji Tomita 1,*, Oliver Couto 2
1 Tokyo Software Company (Inc.), Tokyo, Japan
2 University of Waterloo, Canada
ABSTRACT
Consider the below mentioned equation: x4+y4+z4=·É∗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=·É∗tn--- (A)
KEYWORDS
Quartic Equation, Diophantine Equations, Pure Math, Number Theory, Sums of Powers
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Seiji Tomita , Oliver Couto , "Sum of Three Biquadatics a Multiple of a nth Power, n = (2,3,4,5,6,7,8 & 9)," Universal Journal of Applied Mathematics, Vol. 4, No. 1, pp. 22 - 31, 2016. DOI: 10.13189/ujam.2016.040103.
(b). APA Format:
Seiji Tomita , Oliver Couto (2016). Sum of Three Biquadatics a Multiple of a nth Power, n = (2,3,4,5,6,7,8 & 9). Universal Journal of Applied Mathematics, 4(1), 22 - 31. DOI: 10.13189/ujam.2016.040103.