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Fermat gave the first example of a set of four positive integers {a1, a2, a3, a4} with the property that aiaj + 1 is a square for 1 ≤ i < j ≤ 4. His example was {1, 3, 8, 120}. Baker and Davenport [1] proved that the example could not be extended to a set of 5 positive integers such that the product of any two of them plus one is a square. Kangasabapathy… (More)

- Katalin Gyarmati, Máté Matolcsi, Imre Z. Ruzsa
- Combinatorica
- 2010

For finite sets of integers A1, A2 . . . 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… (More)

- Katalin Gyarmati
- 2008

The aim of this paper is to prove a general version of Plünnecke’s inequality. Namely, assume that for finite sets A, B1, . . . Bk we have information on the size of the sumsets A + Bi1 + · · · + Bil for all choices of indices i1, . . . il. Then we prove the existence of a non-empty subset X of A such that we have ‘good control’ over the size of the sumset… (More)

- Katalin Gyarmati
- Periodica Mathematica Hungarica
- 2004

Three constructions for binary lattices with strong pseudorandom properties are given. These constructions are the two dimensional extensions and modifications of three of the most important one dimensional constructions. The upper estimates for the pseudorandom measures of the binary lattices constructed are based on the principle that character sums in… (More)

- Rudolf Ahlswede, Lars Baumer, +14 authors Zhen Zhang
- GTIT-C
- 2006

The pseudorandom properties of a two dimensional “binary plattice” related to the Legendre symbol are studied.

- Rainer Dietmann, Christian Elsholtz, Katalin Gyarmati, Miklós Simonovits
- J. Comb. Theory, Ser. A
- 2005

- Katalin Gyarmati, C. L. Stewart, Alfred Rényi
- 2007

In this note we give an estimate for the size of a subset A of {1, . . . , N} which has the property that the product of any two distinct elements of A plus 1 is a perfect power.

- Katalin Gyarmati, Christian Mauduit
- Discrete Mathematics
- 2012

This paper concerns the study of the correlation measures of finite binary sequences, more particularily the dependence of correlation measures of even order and correlation measures of odd order. These results generalize previous results due to Gyarmati [7] and to Anantharam [3] and provide a partial answer to a conjecture due to Mauduit [12]. The last… (More)