We prove that for n > 30, every n-th Lucas and Lehmer number has a primitive divisor. This allows us to list all Lucas and Lehmer numbers without a primitive divisor.

Kannan's algorithm for solving the shortest vector problem (SVP) is in particular crucial in Schnorr's celebrated block reduction algorithm, on which rely the best known generic attacks against the lattice-based encryption schemes mentioned above.Expand

Abstract We propose a general method for numerical solution of Thue equations, which allows one to solve in reasonable time Thue equations of high degree (provided necessary algebraic number theory… Expand

18th IEEE Symposium on Computer Arithmetic (ARITH…

25 June 2007

TLDR

The first non-naive algorithm for finding hard to round cases of a periodic function for large floating-point inputs, more precisely when the function cannot be efficiently approximated by a polynomial.Expand