Journals Information
Universal Journal of Applied Mathematics Vol. 4(2), pp. 33 - 38
DOI: 10.13189/ujam.2016.040201
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Methods for Arriving at Numerical Solutions for Equations of the Type (k+3) & (k+5) Bi-quadratic's Equal to a Bi-quadratic (For Different Values of k)
Seiji Tomita 1,*, Oliver Couto 2
1 Tokyo Software Company (Inc), Japan
2 Department of Mathematics, University of Waterloo, Canada
ABSTRACT
Different authors have done analysis regarding sums of powers (Ref. no. 1,2 & 3), but systematic approach for solving Diophantine equations having sums of many bi-quadratics equal to a quartic has not been done before. In this paper we give methods for finding numerical solutions to equation (A) given above in section one. Next in section two, we give methods for finding numerical solutions for equation (B) given above. It is known that finding parametric solutions to biquadratic equations is not easy by conventional method. So the authors have found numerical solutions to equation (A) & (B) using elliptic curve theory.
KEYWORDS
Sums of Powers, Diophantine Equation, Elliptic Curves
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Seiji Tomita , Oliver Couto , "Methods for Arriving at Numerical Solutions for Equations of the Type (k+3) & (k+5) Bi-quadratic's Equal to a Bi-quadratic (For Different Values of k)," Universal Journal of Applied Mathematics, Vol. 4, No. 2, pp. 33 - 38, 2016. DOI: 10.13189/ujam.2016.040201.
(b). APA Format:
Seiji Tomita , Oliver Couto (2016). Methods for Arriving at Numerical Solutions for Equations of the Type (k+3) & (k+5) Bi-quadratic's Equal to a Bi-quadratic (For Different Values of k). Universal Journal of Applied Mathematics, 4(2), 33 - 38. DOI: 10.13189/ujam.2016.040201.