Y. Fujita

activity

20102020

collaborators

4 papers

math.NT2020

The extension of the $D (- k)$ -pair ${k, k + 1}$ to a quadruple

Nikola Adžaga, Alan Filipin, Yasutsugu Fujita

Let $k$ be a positive integer. In this paper, we prove that if ${k, k + 1, c, d}$ is a $D (- k)$ -quadruple with $c > 1$ , then $d = 1$ .

math.NT2017

The Mordell-Weil bases for the elliptic curve of the form $y^{2} = x^{3} - m^{2} x + n^{2}$

Yasutsugu Fujita, Tadahisa Nara

Let $E_{m, n}$ be an elliptic curve over $Q$ of the form $y^{2} = x^{3} - m^{2} x + n^{2}$ , where $m$ and $n$ are positive integers. Brown and Myers showed that the curve $E_{1, n}$ has ra…

math.NT2016

Two-parameter families of uniquely extendable Diophantine triples

Mihai Cipu, Yasutsugu Fujita, Maurice Mignotte

Let A,K be positive integers and u=-2,-1,1 or 2. The main contribution of the paper is a proof that each of the D(u^2)-triples {K,A^2K+2uA,(A+1)^2K+2u(A+1)} has unique extension to…

math.NT2010

On the Mordell--Weil group of the elliptic curve y^2=x^3+n

Yasutsugu Fujita, Tadahisa Nara

We study an infinite family of Mordell curves (i.e. the elliptic curves in the form y^2=x^3+n, n \in Z) over Q with three explicit integral points. We show that the points are inde…

The extension of the D(−k)-pair {k,k+1} to a quadruple

The Mordell-Weil bases for the elliptic curve of the form y2=x3−m2x+n2

Two-parameter families of uniquely extendable Diophantine triples

On the Mordell--Weil group of the elliptic curve y^2=x^3+n

The extension of the $D (- k)$ -pair ${k, k + 1}$ to a quadruple

The Mordell-Weil bases for the elliptic curve of the form $y^{2} = x^{3} - m^{2} x + n^{2}$