Amir Ghadermarzi

activity

20132022

most citedMordell's equation : a classical approach

14 citations · 14 across the 3 of their papers we have counts for

collaborators

5 papers

math.NT2022

Multiples of integral points on Mordell curves

Amir Ghadermarzi

Let $B$ be a sixth-power-free integer and $P$ be a non-torsion point on the Mordell curve $E_{B} : y^{2} = x^{3} + B$ . In this paper, we study integral multiples $[n] P$ of $P$ . Among other res…

math.NT2020

On The Exceptional solutions of Jeśmanowicz' conjecture

Amir Ghadermarzi

Let $(a, b, c)$ be a primitive Pythagorean triple. Set $a = m^{2} - n^{2}$ , $b = 2 mn$ , and $c = m^{2} + n^{2}$ with $m$ and $n$ positive coprime integers, $m > n$ and $m \neq \equiv n (mod 2)$ . A famou…

math.NT2017

On the factorization of $x^{2} + D$

Amir Ghadermarzi

Let $D$ be a positive nonsquare integer, $p$ a prime number with $p ∤ D$ , and $0 < σ < 0.847$ . We show that if the equation $x^{2} + D = p^{n}$ has a huge solution $(x_{0}, n_{0})_{(p, σ)}$ , t…

math.NT2014

Extremal families of cubic Thue equations

Michael A. Bennett, Amir Ghadermarzi

We exactly determine the integral solutions to a previously untreated infinite family of cubic Thue equations of the form $F (x, y) = 1$ with at least $5$ such solutions. Our approach…

math.NT2013★ 14 cited

Mordell's equation : a classical approach

Michael A. Bennett, Amir Ghadermarzi

We solve the Diophantine equation $Y^{2} = X^{3} + k$ for all nonzero integers $k$ with $∣ k ∣ \leq 1 0^{7}$ . Our approach uses a classical connection between these equations and cubic Thue equ…

Multiples of integral points on Mordell curves

On The Exceptional solutions of Jeśmanowicz' conjecture

On the factorization of x2+D

Extremal families of cubic Thue equations

Mordell's equation : a classical approach

On the factorization of $x^{2} + D$