64 citations · 329 across the 206 of their papers we have counts for
10 papers · 1 filter
On the Convex Hull of the Points on Modular Hyperbolas
Sergei V. Konyagin, Igor E. Shparlinski
Given integers and , let $\Hm$ be the following set of integral points $$ \Hm= \{(x,y) \ : \ xy \equiv a \pmod m,\ 1\le x,y \le m-1\} $$ We improve several previously k…
On numbers dividing the th term of a linear recurrence
Juan Jose Alba Gonzalez, Florian Luca, Carl Pomerance +1
Here, we give upper and lower bounds on the count of positive integers dividing the th term of a nondegenerate linearly recurrent sequence with simple roots.
On Pseudopoints of Algebraic Curves
Reza R. Farashahi, Igor E. Shparlinski
Following Kraitchik and Lehmer, we say that a positive integer is an -pseudosquare if it is a quadratic residue for each odd prime , yet is not a squar…
Pseudorandom Bits From Points on Elliptic Curves
Reza R. Farashahi, Igor E. Shparlinski
Let $\E$ be an elliptic curve over a finite field $\F_{q}$ of elements, with , given by an affine Weierstraß equation. We also use to denote the -compone…
On Small Solutions to Quadratic Congruences
Igor Shparlinski
We estimate the deviation of the number of solutions of the congruence from its expected value on average over…
On group structures realized by elliptic curves over arbitrary finite fields
William D. Banks, Francesco Pappalardi, Igor E. Shparlinski
We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at…