Journals Information
Universal Journal of Applied Mathematics Vol. 4(3), pp. 55 - 65
DOI: 10.13189/ujam.2016.040303
Reprint (PDF) (298Kb)
Parametric Solutions to (six) nth Powers Equal to Another (six) nth Powers for Degree 'n' = 2,3,4,5,6,7,8,& 9
Seiji Tomita 1, Oliver Couto 2,*
1 Computer Engineer, Tokyo software co. Inc., Japan
2 University of Waterloo, Waterloo, Ontario, Canada
ABSTRACT
Consider the below mentioned equation: [an+bn+cn+dn+en+fn] = [pn+qn+rn+sn+tn+un]-----(A) Historically in math literature there are instances where solutions have been arrived at by different authors for equation (A) above. Ref. no. (1) by A. Bremner & J. Delorme and Ref. no. (10) by Tito Piezas. The difference is that this article has done systematic analysis of equation (A) for n=2,3,4,5,6,7,8 & 9. While numerical solutions for equation (A) is available on "Wolfram math" website, search for parametric solutions to equation (A) in various publications for all n=2,3,4,5,6,7,8 & 9 did not yield much success. The authors of this paper have selected six terms on each side of equation (A) since the difficulty of the problem increases every time a term is deleted on each side of equation (A). The authors have provided parametric solutions for equation (A) for n=2, 3, 4, 5 & 6 and for n=7, 8 & 9 solutions using elliptical curve theory has been provided. Also we would like to mention that solutions for n=7, 8 & 9 have infinite numerical solutions.
KEYWORDS
Pure Math, Diophantine Equations, Equal Sums, Parametric Solutions
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Seiji Tomita , Oliver Couto , "Parametric Solutions to (six) nth Powers Equal to Another (six) nth Powers for Degree 'n' = 2,3,4,5,6,7,8,& 9," Universal Journal of Applied Mathematics, Vol. 4, No. 3, pp. 55 - 65, 2016. DOI: 10.13189/ujam.2016.040303.
(b). APA Format:
Seiji Tomita , Oliver Couto (2016). Parametric Solutions to (six) nth Powers Equal to Another (six) nth Powers for Degree 'n' = 2,3,4,5,6,7,8,& 9. Universal Journal of Applied Mathematics, 4(3), 55 - 65. DOI: 10.13189/ujam.2016.040303.