@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:34178382,
	title = {Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts},
	url = {https://m2.mtmt.hu/api/publication/34178382},
	author = {Pethő, Attila and Szalay, László},
	doi = {10.15446/recolma.v56n2.108374},
	journal-iso = {REV COLOMBIANA MAT},
	journal = {REVISTA COLOMBIANA DE MATEMÁTICAS},
	volume = {56},
	unique-id = {34178382},
	issn = {0034-7426},
	abstract = {In this paper, we provide an explicit upper bound on the absolute value of the solutions n < m < 0 to the Diophantine equation F(k)n = ±F(k)m, assuming k is even. Here {F(k)n}n ∈ Z denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.},
	year = {2023},
	eissn = {2357-4100},
	pages = {179-187}
}

@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:33044125,
	title = {Rotation on the digital plane},
	url = {https://m2.mtmt.hu/api/publication/33044125},
	author = {Hannusch, Carolin and Pethő, Attila},
	doi = {10.1007/s10998-022-00480-8},
	journal-iso = {PERIOD MATH HUNG},
	journal = {PERIODICA MATHEMATICA HUNGARICA},
	volume = {86},
	unique-id = {33044125},
	issn = {0031-5303},
	abstract = {Let A_{\varphi } A φ denote the matrix of rotation with angle \varphi φ of the Euclidean plane, FLOOR the function which rounds a real point to the nearest lattice point down on the left and ROUND the function for rounding off a vector to the nearest node of the lattice. We prove under the natural assumption \varphi \not = k\frac{\pi }{2} φ ≠ k π 2 that the functions {{\,\mathrm{FLOOR}\,}}\circ A_{\varphi } FLOOR ∘ A φ and {{\,\mathrm{ROUND}\,}}\circ A_{\varphi } ROUND ∘ A φ are neither surjective nor injective. More precisely we prove lower and upper estimates for the size of the sets of lattice points, which are the image of two lattice points as well as of lattice points, which have no preimages. It turns out that the densities of those sets are positive.},
	year = {2023},
	eissn = {1588-2829},
	pages = {564-577}
}

@article{MTMT:33578039,
	title = {Common values of a class of linear recurrences},
	url = {https://m2.mtmt.hu/api/publication/33578039},
	author = {Pethő, Attila},
	doi = {10.1016/j.indag.2022.07.002},
	journal-iso = {INDAGAT MATH NEW SER},
	journal = {INDAGATIONES MATHEMATICAE-NEW SERIES},
	volume = {33},
	unique-id = {33578039},
	issn = {0019-3577},
	abstract = {Let (an), (bn) be linear recursive sequences of integers with characteristic polynomials A(X), B(X) is an element of Z[X] respectively. Assume that A(X) has a dominating and simple real root alpha, while B(X) has a pair of conjugate complex dominating and simple roots C, C over line . Assume further that alpha, C, alpha/C and C over line /C are not roots of unity and delta = log |C|/log |alpha| is an element of Q. Then there are effectively computable constants c0, c1 > 0 such that the inequality|an - bm| > |an|1-(c0 log2 n)/nholds for all n, m is an element of Z2 >= 0 with max{n, m} > c1. We present c0 explicitly.(c) 2022 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.},
	keywords = {Linear recurrences; Baker?s method},
	year = {2022},
	eissn = {1872-6100},
	pages = {1172-1188}
}

@misc{MTMT:32661332,
	title = {Common values of a class of linear recurrence},
	url = {https://m2.mtmt.hu/api/publication/32661332},
	author = {Pethő, Attila},
	unique-id = {32661332},
	year = {2021}
}

@article{MTMT:32163849,
	title = {Formal Language Identity-based Cryptography},
	url = {https://m2.mtmt.hu/api/publication/32163849},
	author = {Vécsi, Ádám and Pethő, Attila},
	doi = {10.21857/y54jofkjdm},
	journal-iso = {RAD HRVAT AKAD ZNAN UMJET MAT ZNAN},
	journal = {RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI},
	volume = {25},
	unique-id = {32163849},
	issn = {1845-4100},
	year = {2021},
	eissn = {1849-2215},
	pages = {143-159}
}

@article{MTMT:32123661,
	title = {Duplications in the k-generalized Fibonacci sequences},
	url = {https://m2.mtmt.hu/api/publication/32123661},
	author = {Luca, Florian and Pethő, Attila and Szalay, László},
	journal-iso = {NEW YORK J MATH},
	journal = {NEW YORK JOURNAL OF MATHEMATICS},
	volume = {27},
	unique-id = {32123661},
	issn = {1076-9803},
	abstract = {Let k >= 3 be an odd integer. Consider the k-generalized Fibonacci sequence backward. The characteristic polynomial of this sequence has no dominating zero, therefore the application of Baker's method becomes more difficult. In this paper, we investigate the coincidence of the absolute values of two terms. The principal theorem gives a lower bound for the difference of two terms (in absolute value) if the larger subscript of the two terms is large enough. A corollary of this theorem makes possible to bound the coincidences in the sequence. The proof essentially depends on the structure of the zeros of the characteristic polynomial, and on the application of linear forms in the logarithms of algebraic numbers. Then we reduced the theoretical bound in practice for 3 <= k <= 99, and determined all the coincidences in the corresponding sequences. Finally, we explain certain patterns of pairwise occurrences in each sequence depending on k if k exceeds a suitable entry value associated to the pair.},
	keywords = {k-generalized Fibonacci sequence},
	year = {2021},
	pages = {1115-1133}
}

@article{MTMT:32007902,
	title = {On k-generalized Fibonacci numbers with negative indices},
	url = {https://m2.mtmt.hu/api/publication/32007902},
	author = {Pethő, Attila},
	doi = {10.5486/PMD.2021.8912},
	journal-iso = {PUBL MATH DEBRECEN},
	journal = {PUBLICATIONES MATHEMATICAE DEBRECEN},
	volume = {98},
	unique-id = {32007902},
	issn = {0033-3883},
	year = {2021},
	eissn = {2064-2849},
	pages = {401-418}
}

@inproceedings{MTMT:31992256,
	title = {On diophantine properties of radix representation in algebraic number fields},
	url = {https://m2.mtmt.hu/api/publication/31992256},
	author = {Pethő, Attila},
	booktitle = {Lie Groups, Number Theory, and Vertex Algebras},
	unique-id = {31992256},
	abstract = {In these notes we investigate elements with special patterns in their representations in number systems in algebraic number fields. We concentrate on periodicity and on the representation of rational integers. We prove under natural assumptions that there are only finitely many S-integers whose representation is periodic with a fixed period. We prove that the same holds for the set of values of polynomials at rational integers.},
	keywords = {Radix representation; Unit equations; number system; Repunits; Periodic words},
	year = {2021},
	pages = {133-148}
}