Katalin Gyarmati

On a family of pseudorandom binary sequences

Recently, numerous constructions have been given for finite pseudorandom binary sequences. However, in many applications, e.g., in cryptography one needs “large’’ families of “good’’ pseudorandom sequences. Very Recently L.~Goubin, C.~Mauduit, A.~Sárkőzy succeeded in constructing large families of pseudorandom binary sequences based on the Legendre symbol. In this paper we will generate another type of large family of pseudorandom sequences by using the notion of index (discrete logarithm).

A superadditivity and submultiplicativity property for cardinalities of sumsets

For finite sets of integers A1,…,An we study the cardinality of the n-fold sumset A1+…+ An compared to those of (n−1)-fold sumsets A1+…+Ai−1+Ai+1+…+An. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets.

Density and ramsey type results on algebraic equations with restricted solution sets

In earlier papers Sárközy studied the solvability of the equations

Plünnecke’s Inequality for Different Summands

a + b = cd, a \in \mathcal{A}, b \in \mathcal{B}, c \in \mathcal{C}, d \in \mathcal{D},

ON THE COMPLEXITY OF A FAMILY RELATED TO THE LEGENDRE SYMBOL

resp.

Shifted products that are coprime pure powers

ab + 1 = cd, a \in \mathcal{A}, b \in \mathcal{B}, c \in \mathcal{C}, d \in \mathcal{D}