@article{MTMT:34742825, title = {Explicit bounds for the solutions of superelliptic equations over number fields}, url = {https://m2.mtmt.hu/api/publication/34742825}, author = {Bérczes, Attila and Yann, Bugeaud and Győry, Kálmán and Jorge, Mello and Alina, Ostafe and Min, Sha}, doi = {10.1515/forum-2023-0381}, journal-iso = {FORUM MATH}, journal = {FORUM MATHEMATICUM}, volume = {2024}, unique-id = {34742825}, issn = {0933-7741}, keywords = {height function; Baker's method; superelliptic equations; Thue equation}, year = {2024}, eissn = {1435-5337}, pages = {1} } @article{MTMT:34742592, title = {Decomposable Forms Generated by Linear Recurrences}, url = {https://m2.mtmt.hu/api/publication/34742592}, author = {Győry, Kálmán and Pethő, Attila and Szalay, László}, journal-iso = {J INTEGER SEQ}, journal = {JOURNAL OF INTEGER SEQUENCES}, volume = {27}, unique-id = {34742592}, abstract = {Consider k ≥ 2 distinct, linearly independent, homogeneous linear recurrences of order k satisfying the same recurrence relation. We prove that the recurrences are related to a decomposable form of degree k, and there is a general identity with a suitable exponential expression depending on the recurrences. This identity is a common and very broad generalization of several known identities. Further, if the recurrences are integer sequences, then the diophantine equation associated with the decomposable form and the exponential term has infinitely many integer solutions generated by the terms of the recurrences. We describe a method for the complete factorization of the decomposable form. Both the form and its decomposition are explicitly given if k = 2, and we present a typical example for k = 3. The basic tool we use is the matrix method. © 2024, University of Waterloo. All rights reserved.}, keywords = {Diophantine equation; Linear recurrence; matrix method; decomposable form; general identity}, year = {2024}, eissn = {1530-7638} } @article{MTMT:34571695, title = {Improved bounds for some S-unit equations}, url = {https://m2.mtmt.hu/api/publication/34571695}, author = {Győry, Kálmán and Le Fourn, Samuel}, doi = {10.4064/aa230530-24-8}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {2024}, unique-id = {34571695}, issn = {0065-1036}, year = {2024}, eissn = {1730-6264}, pages = {1} } @article{MTMT:34123940, title = {On power values of pyramidal numbers, II}, url = {https://m2.mtmt.hu/api/publication/34123940}, author = {Dujella, Andrej and Győry, Kálmán and P, Michaud-Jacobs and Pintér, Ákos}, doi = {10.4064/aa211213-27-7}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {208}, unique-id = {34123940}, issn = {0065-1036}, keywords = {binomial Thue equations; pyramidal; Frey curve; perfect power; modular method; level-lowering}, year = {2023}, eissn = {1730-6264}, pages = {199-213} } @misc{MTMT:34064562, title = {Decomposable form generated by linear recurrences}, url = {https://m2.mtmt.hu/api/publication/34064562}, author = {Győry, Kálmán and Pethő, Attila and Szalay, László}, unique-id = {34064562}, year = {2023} } @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:32337956, title = {Hermite equivalence of polynomials}, url = {https://m2.mtmt.hu/api/publication/32337956}, author = {Manjul, Bhargava and Jan-Hendrik, Evertse and Győry, Kálmán and Remete, László and Ashvin, A. Swaminathan}, doi = {10.4064/aa211113-12-11}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {209}, unique-id = {32337956}, issn = {0065-1036}, year = {2023}, eissn = {1730-6264}, pages = {17-58} } @misc{MTMT:34064339, title = {Improved bounds on some S-unit equations}, url = {https://m2.mtmt.hu/api/publication/34064339}, author = {Samuel, Le Fourn and Győry, Kálmán}, unique-id = {34064339}, year = {2022} } @misc{MTMT:33880992, title = {Multiplicative dependence of rational values modulo approximate finitely generated groups}, url = {https://m2.mtmt.hu/api/publication/33880992}, author = {Bérczes, Attila and Yann, Bugeaud and Győry, Kálmán and Jorge, Mello and Alina, Ostafe and Min, Sha}, unique-id = {33880992}, year = {2022} } @{MTMT:32844418, title = {Baker, Alan (1939–2018), mathematician}, url = {https://m2.mtmt.hu/api/publication/32844418}, author = {Bollobás, Béla and Győry, Kálmán}, booktitle = {Oxford Dictionary of National Biography}, doi = {10.1093/odnb/9780198614128.013.90000380408}, unique-id = {32844418}, year = {2022} }