7 papers
Diophantine equation of degree sixteen
Oliver Couto, Seiji Tomita
While there is not much publications, about degree sixteen Diophantine equation we do have an identity given by Ramanujan (ref. #1). Also on the internet even though there are nume…
Furthur developements regarding Euler equation xyz(x+y+z)=a
Seiji Tomita, Oliver Couto
In this paper, we derived the parametric solution of Euler and Elkies, xyz(x+y+z) = a, in an elementary manner. In addition we proved there are infinitely many parametric solutions…
Diophantine Equation
Seiji Tomita, Oliver Couto
In 2016 Izadi and Nabardi (b) showed (4-2-4) has infinitely many integer solutions. They used a specific congruent number elliptic curve.In 2019 Janfada and Nabardi,item C, showed…
Simultaneous Diophantine Equations
Seiji Tomita, Oliver Couto
This paper gives parametric solutions to quartic equations of the type,(4-3-3),(4-4-4),(4-5-5) and (4-6-6), According to Lander, Parkin, and Selfridge (2) conjecture, there are non…
Methods for arriving at numerical solutions for equations of the type [k+3] and [k+5] biquadratics equal to a bi-quadratic for different values of k
Seiji Tomita, Oliver Couto
Different authors have done analysis regarding sums of powers References number 1,2 and 3, but systematic approach for solving Diophantine equations having sums of many biquadratic…
Parametric Solution to six n degree powers for degree two, three, four, five, six , seven, eight, and nine
Oliver Couto, Seiji Tomita
Historically in math literature there are instances where solutions have been arrived at by different authors for equation 1 for six powers on both side of equation, for different…
A new diophantine equation involving fifth powers
Ajai Choudhry, Oliver Couto
In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation . Further, we show, using ellipti…