Samir Siksek

activity

20142022

most citedShifted powers in binary recurrence sequences

7 citations · 9 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2022★ 2 cited

$Q$ -curves and the Lebesgue-Nagell equation

Michael A. Bennett, Philippe Michaud-Jacobs, Samir Siksek

In this paper, we consider the equation \[ x^2 - q^{2k+1} = y^n, \qquad q \nmid x, \quad 2 \mid y, \] for integers $x, q, k, y$ and $n$ , with $k \geq 0$ and $n \geq 3$ . We extend work…

math.NT2018

On asymptotic Fermat over the Z_2 extension of Q

Nuno Freitas, Alain Kraus, Samir Siksek

In a recent work the authors prove the effective asymptotic Fermat's Last Theorem for the infinite family of fields $Q (ζ_{2^{r + 2}})^{+}$ where $r \geq 0$ . A crucial step in t…

math.NT2014★ 7 cited

Shifted powers in binary recurrence sequences

Michael A. Bennett, Sander R. Dahmen, Maurice Mignotte +1

Let $u_{k}$ be a Lucas sequence. A standard technique for determining the perfect powers in the sequence $u_{k}$ combines bounds coming from linear forms in logarithms with local infor…

Q-curves and the Lebesgue-Nagell equation

On asymptotic Fermat over the Z_2 extension of Q

Shifted powers in binary recurrence sequences

$Q$ -curves and the Lebesgue-Nagell equation