12 citations · 70 across the 40 of their papers we have counts for
14 papers · 1 filter
On Pseudosquares and Pseudopowers
Carl Pomerance, Igor E. Shparlinski
Introduced by Kraitchik and Lehmer, an -pseudosquare is a positive integer that is a quadratic residue for each odd prime , yet is not a square. We use…
On the Convex Closure of the Graph of Modular Inversions
Mizan R. Khan, Igor E. Shparlinski, Christian L. Yankov
In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set $$ G_n=\left\{(a,b) : a,b\in \Z, ab \equiv 1…
Arithmetic and Geometric Progressions in Productsets over Finite Fields
Igor E. Shparlinski
Given two sets $\cA, \cB \subseteq \F_q$ of elements of the finite field $\F_q$ of elements, we show that the productset $$ \cA\cB = \{ab | a \in \cA, b \in\cB\} $$ contains an…
On RSA Moduli with Almost Half of the Bits Prescribed
Sidney W. Graham, Igor E. Shparlinski
We show that using character sum estimates due to H. Iwaniec leads to an improvement of recent results about the distribution and finding RSA moduli , where and are p…
On The Solvability of Bilinear Equations in Finite Fields
Igor E. Shparlinski
We consider the equation over a finite field of elements, with variables from arbitrary sets $ A, B, C, D \sub…
Products in Residue Classes
John B. Friedlander, Par Kurlberg, Igor E. Shparlinski
We consider a problem of P. Erdos, A. M. Odlyzko and A. Sarkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that ev…