TY - JOUR AU - Bertók, Csanád AU - Hajdu, Lajos TI - The resolution of three exponential Diophantine equations in several variables JF - JOURNAL OF NUMBER THEORY J2 - J NUMBER THEORY VL - 260 PY - 2024 SP - 29 EP - 40 PG - 12 SN - 0022-314X DO - 10.1016/j.jnt.2024.01.009 UR - https://m2.mtmt.hu/api/publication/34781671 ID - 34781671 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Sebestyén, Péter TI - Terms of recurrence sequences in the solution sets of norm form equations JF - ARCHIV DER MATHEMATIK J2 - ARCH MATH VL - 122 PY - 2024 SP - 179 EP - 187 PG - 9 SN - 0003-889X DO - 10.1007/s00013-023-01941-3 UR - https://m2.mtmt.hu/api/publication/34399660 ID - 34399660 AB - The structure as well as several arithmetic properties of the solution sets of norm form equations are of classical and recent interest. In this paper, we give a finiteness result for terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations. Our main theorem yields a common generalization of certain recent results from the literature. LA - English DB - MTMT ER - TY - JOUR AU - Ceko, Matthew AU - Hajdu, Lajos AU - Tijdeman, Rob TI - Error Correction for Discrete Tomography JF - FUNDAMENTA INFORMATICAE J2 - FUND INFOR VL - 189 PY - 2023 IS - 2 SP - 91 EP - 112 PG - 22 SN - 0169-2968 DO - 10.3233/FI-222154 UR - https://m2.mtmt.hu/api/publication/34244476 ID - 34244476 AB - Discrete tomography focuses on the reconstruction of functions from their line sums in a finite number d of directions. In this paper we consider functions f : A -> R where A is a finite subset of Z(2) and R an integral domain. Several reconstruction methods have been introduced in the literature. Recently Ceko, Pagani and Tijdeman developed a fast method to reconstruct a function with the same line sums as f. Up to here we assumed that the line sums are exact. Some authors have developed methods to recover the function f under suitable conditions by using the redundancy of data. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than d/2 errors can be corrected and that this bound is the best possible. Moreover, we prove that if it is known that the line sums in k given directions are correct, then the line sums in every other direction can be corrected provided that the number of wrong line sums in that direction is less than k/2. LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Tijdeman, Robert AU - Varga, Nóra TI - On polynomials with only rational roots JF - MATHEMATIKA J2 - MATHEMATIKA VL - 69 PY - 2023 IS - 3 SP - 867 EP - 878 PG - 12 SN - 0025-5793 DO - 10.1112/mtk.12209 UR - https://m2.mtmt.hu/api/publication/34069923 ID - 34069923 AB - In this paper, we study upper bounds for the degrees of polynomials with only rational roots. First, we assume that the coefficients are bounded. In the second theorem, we suppose that the primes 2 and 3 do not divide any coefficient. The third theorem concerns the case that all coefficients are composed of primes from a fixed finite set. LA - English DB - MTMT ER - TY - JOUR AU - Bérczes, Attila AU - Hajdu, Lajos AU - Luca, Florian AU - Pink, István TI - Additive Diophantine Equations with Binary Recurrences, S-Units and Several Factorials JF - RESULTS IN MATHEMATICS J2 - RES MATHEM VL - 78 PY - 2023 IS - 4 PG - 32 SN - 1422-6383 DO - 10.1007/s00025-023-01871-0 UR - https://m2.mtmt.hu/api/publication/33843349 ID - 33843349 AB - There are many results in the literature concerning linear combinations of factorials among terms of linear recurrence sequences. Recently, Grossman and Luca provided effective bounds for such terms of binary recurrence sequences. In this paper we show that under certain conditions, even the greatest prime divisor of u(n) - a(1)m(1)! - . . . - a(k)m(k)! tends to infinity, in an effective way. We give some applications of this result, as well. LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Tijdeman, R. TI - The Diophantine equation $f(x)=g(y)$ for polynomials with simple rational roots JF - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY J2 - J LOND MATH SOC VL - 108 PY - 2023 IS - 1 SP - 309 EP - 339 PG - 31 SN - 0024-6107 DO - 10.1112/jlms.12746 UR - https://m2.mtmt.hu/api/publication/33841313 ID - 33841313 AB - In this paper we consider Diophantine equations of the form f(x)=g(y)$f(x)=g(y)$ where f$f$ has simple rational roots and g$g$ has rational coefficients. We give strict conditions for the cases where the equation has infinitely many solutions in rationals with a bounded denominator. We give examples illustrating that the given conditions are necessary. It turns out that such equations with infinitely many solutions are strongly related to Prouhet-Tarry-Escott tuples. In the special, but important case when g$g$ has only simple rational roots as well, we can give a simpler statement. Also we provide an application to equal products with terms belonging to blocks of consecutive integers of bounded length. The latter theorem is related to problems and results of Erdos and Turk, and of Erdos and Graham. LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Tijdeman, Robert AU - Varga, Nóra TI - Diophantine equations for Littlewood polynomials JF - ACTA ARITHMETICA J2 - ACTA ARITH VL - 210 PY - 2023 SP - 223 EP - 234 PG - 12 SN - 0065-1036 DO - 10.4064/aa220912-3-11 UR - https://m2.mtmt.hu/api/publication/33704865 ID - 33704865 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Herendi, Orsolya TI - Extrema of polynomials with real roots and Diophantine equations JF - JOURNAL OF NUMBER THEORY J2 - J NUMBER THEORY VL - 242 PY - 2023 SP - 626 EP - 646 PG - 21 SN - 0022-314X DO - 10.1016/j.jnt.2022.05.004 UR - https://m2.mtmt.hu/api/publication/33025271 ID - 33025271 LA - English DB - MTMT ER - TY - JOUR AU - Győry, Kálmán AU - Hajdu, Lajos AU - Sárközy, András TI - On additive and multiplicative decompositions of sets of integers composed from a given set of primes, II (multiplicative decompositions) JF - ACTA ARITHMETICA J2 - ACTA ARITH VL - 210 PY - 2023 SP - 191 EP - 204 PG - 14 SN - 0065-1036 DO - 10.4064/aa220805-13-6 UR - https://m2.mtmt.hu/api/publication/32844207 ID - 32844207 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Papp, Ágoston TI - Uniform bounds for the number of powers in arithmetic progressions JF - REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS J2 - RACSAM REV R ACAD A VL - 116 PY - 2022 IS - 4 PG - 7 SN - 1578-7303 DO - 10.1007/s13398-022-01313-6 UR - https://m2.mtmt.hu/api/publication/33158512 ID - 33158512 AB - We give sharp, in some sense uniform bounds for the number of l-th powers and arbitrary powers among the first N terms of an arithmetic progression, for N large enough. LA - English DB - MTMT ER -