@article{MTMT:32844207, title = {On additive and multiplicative decompositions of sets of integers composed from a given set of primes, II (multiplicative decompositions)}, url = {https://m2.mtmt.hu/api/publication/32844207}, author = {Győry, Kálmán and Hajdu, Lajos and Sárközy, András}, doi = {10.4064/aa220805-13-6}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {210}, unique-id = {32844207}, issn = {0065-1036}, year = {2023}, eissn = {1730-6264}, pages = {191-204}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:32548302, title = {On additive and multiplicative decompositions of sets of integers composed from a given set of primes, I (Additive decompositions)}, url = {https://m2.mtmt.hu/api/publication/32548302}, author = {Győry, Kálmán and Hajdu, Lajos and Sárközy, András}, doi = {10.4064/aa210309-14-6}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {202}, unique-id = {32548302}, issn = {0065-1036}, year = {2022}, eissn = {1730-6264}, pages = {29-42}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:31967722, title = {On additive and multiplicative decompositions of sets of integers with restricted prime factors, II: Smooth numbers and generalizations}, url = {https://m2.mtmt.hu/api/publication/31967722}, author = {Győry, Kálmán and Hajdu, Lajos and Sárközy, András}, doi = {10.1016/j.indag.2021.05.001}, journal-iso = {INDAGAT MATH NEW SER}, journal = {INDAGATIONES MATHEMATICAE-NEW SERIES}, volume = {32}, unique-id = {31967722}, issn = {0019-3577}, abstract = {In part I of this paper we studied additive decomposability of the set Fy of the y-smooth numbers and the multiplicative decomposability of the shifted set Gy=Fy+{1}. In this paper, focusing on the case of ’large’ functions y, we continue the study of these problems. Further, we also investigate a problem related to the m-decomposability of k-term sumsets, for arbitrary k. © 2021 The Author(s)}, year = {2021}, eissn = {1872-6100}, pages = {813-823}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:31669838, title = {On additive and multiplicative decompositions of sets of integers with restricted prime factors, I.. (Smooth numbers)}, url = {https://m2.mtmt.hu/api/publication/31669838}, author = {Győry, Kálmán and Hajdu, Lajos and Sárközy, András}, doi = {10.1016/j.indag.2020.10.007}, journal-iso = {INDAGAT MATH NEW SER}, journal = {INDAGATIONES MATHEMATICAE-NEW SERIES}, volume = {32}, unique-id = {31669838}, issn = {0019-3577}, year = {2021}, eissn = {1872-6100}, pages = {365-374}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:31454838, title = {On multiplicative decompositions of polynomial sequences, III}, url = {https://m2.mtmt.hu/api/publication/31454838}, author = {Hajdu, Lajos and Sárközy, András}, doi = {10.4064/aa190410-23-7}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {193}, unique-id = {31454838}, issn = {0065-1036}, abstract = {In two earlier papers we studied the multiplicative decomposability of polynomial sequences {f(x):x∈Z,f(x)>0}. Here we extend this problem by considering also sequences which can be obtained from sequences of this type by changing “not too many” elements of them. In particular, we prove the multiplicative analogue of a theorem of Szemerédi and the second author (related to a problem of Erdős).}, keywords = {continued fractions; shifted powers; binomial Thue equations; multiplicative decompositions}, year = {2020}, eissn = {1730-6264}, pages = {193-216}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:31280441, title = {Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)}, url = {https://m2.mtmt.hu/api/publication/31280441}, author = {Borbély, József and Sárközy, András}, doi = {10.2478/udt-2019-0017}, journal-iso = {UNIF DISTRIB THEOR}, journal = {UNIFORM DISTRIBUTION THEORY}, volume = {14}, unique-id = {31280441}, issn = {1336-913X}, year = {2019}, eissn = {2309-5377}, pages = {103-126}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:3343340, title = {On the distribution of the sum of digits of sums a plus b}, url = {https://m2.mtmt.hu/api/publication/3343340}, author = {Mauduit, C and Rivat, J and Sárközy, András}, doi = {10.1007/s11139-017-9977-3}, journal-iso = {RAMANUJAN J}, journal = {RAMANUJAN JOURNAL}, volume = {49}, unique-id = {3343340}, issn = {1382-4090}, abstract = {Let (Formula presented.), (Formula presented.) be large subsets of (Formula presented.). We study the distribution of the sum of binary digits of the sums (Formula presented.) with (Formula presented.). © 2018 Springer Science+Business Media, LLC, part of Springer Nature}, year = {2019}, eissn = {1572-9303}, pages = {55-73}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @inproceedings{MTMT:30501326, title = {The Measures of Pseudorandomness and the NIST Tests}, url = {https://m2.mtmt.hu/api/publication/30501326}, author = {Mérai, László and Rivat, Joel and Sárközy, András}, booktitle = {Number-Theoretic Methods in Cryptology}, doi = {10.1007/978-3-319-76620-1_12}, unique-id = {30501326}, abstract = {A few years ago new quantitative measures of pseudorandomness of binary sequences have been introduced. Since that these measures have been studied in many papers and many constructions have been given along these lines. In this paper the connection between the new measures and the NIST tests is analyzed. It is shown that finite binary sequences possessing strong pseudorandom properties in terms of these new measures usually also pass or nearly pass most of the NIST tests.}, keywords = {Pseudorandom sequences; Binary sequence; NIST tests}, year = {2018}, pages = {197-216}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:30312047, title = {On multiplicative decompositions of polynomial sequences, II}, url = {https://m2.mtmt.hu/api/publication/30312047}, author = {Hajdu, Lajos and Sárközy, András}, doi = {10.4064/aa171116-7-3}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {186}, unique-id = {30312047}, issn = {0065-1036}, keywords = {multiplicative decomposition; shifted powers; polynomial values; binomial Thue equations; ADDITIVE DECOMPOSITIONS}, year = {2018}, eissn = {1730-6264}, pages = {191-200}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} } @article{MTMT:3324468, title = {On multiplicative decompositions of polynomial sequences, I}, url = {https://m2.mtmt.hu/api/publication/3324468}, author = {Hajdu, Lajos and Sárközy, András}, doi = {10.4064/aa170620-13-12}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {184}, unique-id = {3324468}, issn = {0065-1036}, year = {2018}, eissn = {1730-6264}, pages = {139-150}, orcid-numbers = {Sárközy, András/0000-0003-0156-4601} }