We prove that if xm + axn permutes the prime field Fp, where m > n > 0 and a ∈ Fp, then gcd(m − n, p − 1) > √ p − 1. Conversely, we prove that if q ≥ 4 and m > n > 0 are fixed and satisfy gcd(m − n, q − 1) > 2q(log log q)/ log q, then there exist permutation binomials over Fq of the form xm + axn if and only if gcd(m,n, q − 1) = 1.

The atdvent of practical parallel processors has caused a reexamination of many existing algorithms with'the hope of discovering a parallel implementation. One of the oldest and best know algorithms is Euclid's algorithm for computing the greatest common divisor (GCD). In this paper we present a parallel algorithm to compute the GCD of two integers. Although there have been results in the paral...

A new parallel extended GCD algorithm is proposed. It matches the best existing parallel integer GCD algorithms of Sorenson and Chor and Goldreich, since it can be achieved in O (n/ logn) time using at most n1+ processors on CRCW PRAM. Sorenson and Chor and Goldreich both use a modular approach which consider the least significant bits. By contrast, our algorithm only deals with the leading bit...

We demonstrate that the answer to the question posed in the title is “yes” and “no”: “no” if the set of permissible operations is restricted to {+,−,×,/,mod,<}; “yes” if we are also allowed a gcd-oracle as a permissible operation. It has been shown (see [Sto76, MST91]) that no strongly polynomial algorithm exists for the problem of finding the greatest common divisor (gcd) of two arbitrary inte...

In 1991, Weidong Fang and Huiling Li proved that there are only finitely many non-trivial linear spaces that admit a line-transitive, point imprimitive group action, for a given value of gcd(k, r), where k is the line size and r is the number of lines on a point. The aim of this paper is to make that result effective. We obtain a classification of all linear spaces with this property having gcd...

The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvester matrix of lower rank whose entries are near the corresponding entries of that input matrix. We solve the approximate GCD problem by a new method based on structured total least norm (STLN) algorithms...

Granule cell dispersion (GCD) is observed in approximately 40% of cases of hippocampal sclerosis (HS) in patients with epilepsy. Studies in animal models suggest that GCD may be a consequence of enhanced proliferation of granule cell precursors as a result of seizures. We quantified the number of cells in cycle in subfields of the hippocampus with immunohistochemistry for Mcm2 in 14 HS cases wi...

In this paper we examine the applicability of the previously proposed Greatest Common Divisor GCD method to blind image deconvolution In this method the desired image is approximated as the GCD of the two dimensional polynomials corresponding to the z transforms of two or more distorted and noisy versions of the same scene assuming that the distortion lters are FIR and relatively co prime We ju...