Seiji Tomita

activity

20222024

collaborators

5 papers

math.GM2024

On the diophantine equation $X^{6} - Y^{6} = W^{n} - Z^{n}, n = 2, 3, 4$

Seiji Tomita

In this paper, we proved that there are infinitely many integer solutions of $X^{6} - Y^{6} = W^{n} - Z^{n}, n = 2, 3, 4$ .

math.GM2024

A family of Mordell curves with the rank of at least three

Seiji Tomita

We constructed a parametrized family of Mordell curves with the rank of at least three.

math.GM2023

On $A^{4} + h B^{4} = C^{4} + h D^{4}$

Seiji Tomita

In this paper, this author proved that $A^{4} + h B^{4} = C^{4} + h D^{4}$ always has the integral solutions for $h < 20000.$ Then we conjecture the equation $A^{4} + h B^{4} = C^{4} + h D^{4}$ always…

math.GM2022

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…

math.GM2022

Diophantine Equation $n (x^{4} + y^{4}) = z^{4} + w^{4}$

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…

On the diophantine equation X6−Y6=Wn−Zn,n=2,3,4

A family of Mordell curves with the rank of at least three

On A4+hB4=C4+hD4

Furthur developements regarding Euler equation xyz(x+y+z)=a

Diophantine Equation n(x4+y4)=z4+w4

On the diophantine equation $X^{6} - Y^{6} = W^{n} - Z^{n}, n = 2, 3, 4$

On $A^{4} + h B^{4} = C^{4} + h D^{4}$

Diophantine Equation $n (x^{4} + y^{4}) = z^{4} + w^{4}$