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Dive into the research topics where Samir Siksek is active.

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Featured researches published by Samir Siksek.


Compositio Mathematica | 2006

Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation

Yann Bugeaud; Maurice Mignotte; Samir Siksek

We solve completely the Lebesgue-Nagell equation x^2+D=y^n, in integers x, y, n>2, for D in the range 1 =< D =< 100.


Elemente Der Mathematik | 2008

Fibonacci numbers at most one away from a perfect power

Yann Bugeaud; Florian Luca; Maurice Mignotte; Samir Siksek

The famous problem of determining all perfect powers in the Fibonacci sequence and the Lucas sequence has recently been resolved by three of the present authors. We sketch the proof of this result, and we apply it to show that the only Fibonacci numbers Fn such that Fn ± 1 is a perfect power are 0, 1, 2, 3, 5 and 8. The proof of the Fibonacci Perfect Powers Theorem involves very deep mathematics, combining the modular approach used in the proof of Fermat’s Last Theorem with Baker’s Theory. By contrast, using the knowledge of the all perfect powers in the Fibonacci and Lucas sequences, the determination of the perfect powers among the numbers Fn ± 1 is quite elementary.


Journal of Cryptology | 1999

A Fast Diffie--Hellman Protocol in Genus 2

Nigel P. Smart; Samir Siksek

Abstract. In this paper it is shown how the multiplication by M map on the Kummer surface of a curve of genus 2 defined over


Canadian Journal of Mathematics | 2008

A MULTI-FREY APPROACH TO SOME MULTI-PARAMETER FAMILIES OF DIOPHANTINE EQUATIONS

Yann Bugeaud; Maurice Mignotte; Samir Siksek

{\Bbb F}_q


Archive | 2007

The Modular Approach to Diophantine Equations

Samir Siksek

can be used to construct a Diffie—Hellman protocol. We show that this map can be computed using only additions and multiplications in


Crelle's Journal | 2007

Perfect powers from products of terms in Lucas sequences

Yann Bugeaud; Florian Luca; Maurice Mignotte; Samir Siksek

{\Bbb F}_q


Proceedings of the Edinburgh Mathematical Society (Series 2) | 2010

On factorials expressible as sums of at most three Fibonacci numbers

Florian Luca; Samir Siksek

. In particular we do not use any divisions, polynomial arithmetic, or square root functions in


Bulletin of The London Mathematical Society | 2003

ON A SHIMURA CURVE THAT IS A COUNTEREXAMPLE TO THE HASSE PRINCIPLE

Samir Siksek; Alexei N. Skorobogatov

{\Bbb F}_q


Mathematika | 2017

PERFECT POWERS THAT ARE SUMS OF CONSECUTIVE CUBES

Michael A. Bennett; Vandita Patel; Samir Siksek

, hence this may be easier to implement than multiplication by M on the Jacobian. In addition we show that using the Kummer surface does not lead to any loss in security.


arXiv: Number Theory | 2016

Residual representations of semistable principally polarized abelian varieties

Samuele Anni; Pedro Lemos; Samir Siksek

We solve several multi-parameter families of binomial Thue equa- tions of arbitrary degree; for example, we solve the equation

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Yann Bugeaud

University of Strasbourg

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Florian Luca

University of the Witwatersrand

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Michael A. Bennett

University of British Columbia

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