TY - JOUR AU - Szikszai, Márton AU - Ziegler, Volker TI - On arithmetic progressions in Lucas sequences – II JF - JOURNAL OF NUMBER THEORY J2 - J NUMBER THEORY VL - 201 PY - 2019 SP - 354 EP - 376 PG - 23 SN - 0022-314X DO - 10.1016/j.jnt.2019.02.015 UR - https://m2.mtmt.hu/api/publication/30922155 ID - 30922155 AB - In this paper, we provide an effective and practical method to find all three term arithmetic progressions in a given Lucas sequence of the first or second kind. Our interest is the case when the sequence has a negative discriminant, since the case of positive discriminant has recently been resolved by Hajdu et al. [11]. We present a conjecture on the maximal number and length of such arithmetic progressions based on computational evidence. LA - English DB - MTMT ER - TY - THES AU - Szikszai, Márton TI - Coprimality in consecutive terms of integer sequences PB - Debreceni Egyetem Természettudományi Kar PY - 2018 UR - https://m2.mtmt.hu/api/publication/27489404 ID - 27489404 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Szikszai, Márton AU - Volker, Ziegler TI - On arithmetic progressions in Lucas sequences JF - JOURNAL OF INTEGER SEQUENCES J2 - J INTEGER SEQ VL - 20 PY - 2017 IS - 8 PG - 18 SN - 1530-7638 UR - https://m2.mtmt.hu/api/publication/3319168 ID - 3319168 LA - English DB - MTMT ER - TY - JOUR AU - Szikszai, Márton TI - Distinct Products in Lucas Sequences - On a Problem of Kimberling JF - FIBONACCI QUARTERLY J2 - FIBONACCI QUART VL - 55 PY - 2017 IS - 4 SP - 291 EP - 296 PG - 6 SN - 0015-0517 UR - https://m2.mtmt.hu/api/publication/3319166 ID - 3319166 N1 - Institute of Mathematics, University of Debrecen, P.O. Box 400, Debrecen, H-4002, Hungary MTA-DE Research Group 'Equations Functions and Curves', Hungarian Academy of Sciences, University of Debrecen, Hungary Export Date: 16 October 2021 Correspondence Address: Szikszai, M.; Institute of Mathematics, P.O. Box 400, Hungary; email: szikszai.marton@science.unideb.hu LA - English DB - MTMT ER - TY - JOUR AU - Carlo, Sanna AU - Szikszai, Márton TI - A coprimality condition on consecutive values of polynomials JF - BULLETIN OF THE LONDON MATHEMATICAL SOCIETY J2 - B LOND MATH SOC VL - 49 PY - 2017 IS - 5 SP - 908 EP - 915 PG - 8 SN - 0024-6093 DO - 10.1112/blms.12078 UR - https://m2.mtmt.hu/api/publication/3284731 ID - 3284731 LA - English DB - MTMT ER - TY - JOUR AU - Pink, István AU - Szikszai, Márton TI - A Brocard-Ramanujan-type equation with Lucas and associated Lucas sequences JF - GLASNIK MATEMATICKI J2 - GLASNIK MAT VL - 52 PY - 2017 IS - 1 SP - 11 EP - 21 PG - 11 SN - 0017-095X DO - 10.3336/gm.52.1.02 UR - https://m2.mtmt.hu/api/publication/3099616 ID - 3099616 LA - English DB - MTMT ER - TY - JOUR AU - Andrej, Dujella AU - Matija, Kazalicki AU - Miljen, Mikic AU - Szikszai, Márton TI - There are infinitely many rational Diophantine sextuples JF - INTERNATIONAL MATHEMATICS RESEARCH NOTICES J2 - INT MATH RES NOTICES VL - 2017 PY - 2017 IS - 2 SP - 490 EP - 508 PG - 19 SN - 1073-7928 DO - 10.1093/imrn/rnv376 UR - https://m2.mtmt.hu/api/publication/3076850 ID - 3076850 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Laishram, Shanta AU - Szikszai, Márton TI - Perfect powers in products of terms of elliptic divisibility sequences JF - BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY J2 - B AUST MATH SOC VL - 94 PY - 2016 IS - 3 SP - 395 EP - 404 PG - 10 SN - 0004-9727 DO - 10.1017/S0004972716000332 UR - https://m2.mtmt.hu/api/publication/3082686 ID - 3082686 N1 - Institute of Mathematics, University of Debrecen, P.O. Box 400, Debrecen, H-4002, Hungary Stat-Math Unit, Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi, 110016, India Cited By :1 Export Date: 9 June 2023 Correspondence Address: Szikszai, M.; Institute of Mathematics, P.O. Box 400, Hungary; email: szikszai.marton@science.unideb.hu Funding details: Indian National Science Academy, INSA Funding details: Austrian Science Fund, FWF, P24574 Funding details: Hungarian Scientific Research Fund, OTKA, K115479 Funding text 1: L. Hajdu was supported in part by the OTKA grant K115479. S. Laishram was supported in part by INSA, India, HAS, Hungary and FWF (Austrian Science Fund) grant no. P24574. LA - English DB - MTMT ER - TY - CHAP AU - Gál, Zoltán AU - Ágnes, Nagy AU - Szikszai, Márton AU - Terdik, György ED - Emőd, Kovács ED - Gábor, Kusper ED - Roland, Kunkli ED - Tibor, Tómács TI - Stochastic modeling of Wireless Networks. a case study in time domain TS - a case study in time domain T2 - 9th International Conference on Applied Informatics PB - Eszterházy Károly Főiskola (EKF) CY - Eger SN - 9786155297199 PY - 2015 SP - 195 EP - 201 PG - 7 DO - 10.14794/ICAI.9.2014.2.195 UR - https://m2.mtmt.hu/api/publication/3076851 ID - 3076851 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Szikszai, Márton TI - Common factors in series of consecutive terms of associated Lucas and Lehmer sequences JF - FIBONACCI QUARTERLY J2 - FIBONACCI QUART VL - 53 PY - 2015 IS - 3 SP - 221 EP - 229 PG - 9 SN - 0015-0517 UR - https://m2.mtmt.hu/api/publication/2963098 ID - 2963098 N1 - Cited By :2 Export Date: 13 June 2023 Funding details: European Commission, EC Funding details: Hungarian Scientific Research Fund, OTKA, K100339, NK101680 Funding details: European Social Fund, ESF Funding text 1: 1Research supported in part by the OTKA grants K100339 and NK101680. The publication is supported by the TÁMOP-4.2.2.C-11/1/KONV-20102-0001 project. The project has been supported by the European Union, co-financed by the European Social Fund. LA - English DB - MTMT ER -