Samir Siksek
University of Warwick
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Publication
Featured researches published by Samir Siksek.
Compositio Mathematica | 2006
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
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
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
Yann Bugeaud; Maurice Mignotte; Samir Siksek
{\Bbb F}_q
Archive | 2007
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
Yann Bugeaud; Florian Luca; Maurice Mignotte; Samir Siksek
{\Bbb F}_q
Proceedings of the Edinburgh Mathematical Society (Series 2) | 2010
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
Samir Siksek; Alexei N. Skorobogatov
{\Bbb F}_q
Mathematika | 2017
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
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