TY - JOUR AU - Győry, Kálmán AU - Hajdu, Lajos AU - Pintér, Ákos TI - Perfect powers from products of consecutive terms in arithmetic progression JF - COMPOSITIO MATHEMATICA J2 - COMPOS MATH VL - 145 PY - 2009 IS - 4 SP - 845 EP - 864 PG - 20 SN - 0010-437X DO - 10.1112/S0010437X09004114 UR - https://m2.mtmt.hu/api/publication/1138460 ID - 1138460 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Tengely, Szabolcs TI - Arithmetic progressions of squares, cubes and n-th powers JF - FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI J2 - FUNCT APPROX COMMENT MATH VL - 41 PY - 2009 IS - 2 SP - 129 EP - 138 PG - 10 SN - 0208-6573 DO - 10.7169/facm/1261157805 UR - https://m2.mtmt.hu/api/publication/1105972 ID - 1105972 AB - In this paper we continue the investigations about unlike powers in arithmetic progression. We provide sharp upper bounds for the length of primitive non-constant arithmetic progressions consisting of squares/cubes and n-th powers. LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos AU - Tijdeman, R AU - Tengely, Szabolcs TI - Cubes in products of terms in arithmetic progression JF - PUBLICATIONES MATHEMATICAE DEBRECEN J2 - PUBL MATH DEBRECEN VL - 74 PY - 2009 IS - 1-2 SP - 215 EP - 232 PG - 18 SN - 0033-3883 UR - https://m2.mtmt.hu/api/publication/1105971 ID - 1105971 LA - English DB - MTMT ER - TY - JOUR AU - Bennett, MA AU - Bruin, N AU - Győry, Kálmán AU - Hajdu, Lajos TI - Powers from products of consecutive terms in arithmetic progression JF - PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY J2 - P LOND MATH SOC VL - 92 PY - 2006 IS - 2 SP - 273 EP - 306 PG - 34 SN - 0024-6115 DO - 10.1112/S0024611505015625 UR - https://m2.mtmt.hu/api/publication/1098342 ID - 1098342 N1 - Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada Number Theory Research Group, University of Debrecen, Hungarian Academy of Sciences, P.O. Box 12, 4010 Debrecen, Hungary Cited By :36 Export Date: 13 October 2021 Correspondence Address: Bennett, M.A.; Department of Mathematics, , Vancouver, BC V6T 1Z2, Canada; email: bennett@math.ubc.ca Funding details: 3272-13/066/2001, F34981, T29330, T38225, T42985 Funding details: Natural Sciences and Engineering Research Council of Canada, NSERC Funding details: Erwin Schrödinger International Institute for Mathematics and Physics, ESI Funding details: Nederlandse Organisatie voor Wetenschappelijk Onderzoek, NWO Funding details: Magyar Tudományos Akadémia, MTA Funding text 1: Research supported in part by grants from NSERC (M.A.B. and N.B.), the Erwin Schrödinger Institute in Vienna (M.A.B. and K.G.), the Netherlands Organization for Scientific Research (NWO) (K.G. and L.H.), the Hungarian Academy of Sciences (K.G. and L.H.), by FKFP grant 3272-13/066/2001 (L.H.) and by grants T29330, T42985 (K.G. and L.H.), T38225 (K.G.) and F34981 (L.H.) of the Hungarian National Foundation for Scientific Research. LA - English DB - MTMT ER - TY - JOUR AU - Bruin, N AU - Győry, Kálmán AU - Hajdu, Lajos AU - Tengely, Szabolcs TI - Arithmetic progressions consisting of unlike powers JF - INDAGATIONES MATHEMATICAE-NEW SERIES J2 - INDAGAT MATH NEW SER VL - 17 PY - 2006 IS - 4 SP - 539 EP - 555 PG - 17 SN - 0019-3577 DO - 10.1016/S0019-3577(07)00002-X UR - https://m2.mtmt.hu/api/publication/1073987 ID - 1073987 AB - In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given k >= 4 and L >= 3 there are only finitely many arithmetic progressions of the form (x(0)(l0), x(1)(l1),..., x(k-1)(lk-1)) with x(i) epsilon Z, gcd(x(0), x(1))= 1 and 2 <= l(i) <= L for i = 0, 1,...,k - 1. Furthermore, we show that, for L = 3, the progression (1, 1,..., 1) is the only such progression up to sign. Our proofs involve some well-known theorems of Faltings [9], Darmon and Granville [6] as well as Chabauty's method applied to superelliptic curves. LA - English DB - MTMT ER - TY - JOUR AU - Győry, Kálmán AU - Hajdu, Lajos AU - Saradha, N TI - On the diophantine equation n(n+d)...(n+(k-1)d)=by^l JF - CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES J2 - CAN MATH BULL VL - 47 PY - 2004 IS - 3 SP - 373 EP - 388 PG - 16 SN - 0008-4395 DO - 10.4153/CMB-2004-037-1 UR - https://m2.mtmt.hu/api/publication/1092759 ID - 1092759 LA - English DB - MTMT ER - TY - JOUR AU - Hajdu, Lajos TI - Perfect powers in arithmetic progression. A note on the inhomogeneous case JF - ACTA ARITHMETICA J2 - ACTA ARITH VL - 113 PY - 2004 IS - 4 SP - 343 EP - 349 PG - 7 SN - 0065-1036 DO - 10.4064/aa113-4-4 UR - https://m2.mtmt.hu/api/publication/1242196 ID - 1242196 LA - English DB - MTMT ER - TY - JOUR AU - Filakovszky, P AU - Hajdu, Lajos TI - The resolution of the diophantine equation x(x+d)...(x+(k-1)d)=by^2 for fixed d JF - ACTA ARITHMETICA J2 - ACTA ARITH VL - 98 PY - 2001 IS - 2 SP - 151 EP - 154 PG - 4 SN - 0065-1036 DO - 10.4064/aa98-2-5 UR - https://m2.mtmt.hu/api/publication/1242125 ID - 1242125 N1 - Cited By :8 Export Date: 13 October 2021 Correspondence Address: Filakovszky, P.Šoltésovej 21, 94059 Nové Zámky, Slovakia; email: hajdul@math.klte.hu LA - English DB - MTMT ER - TY - JOUR AU - Brindza, B AU - Hajdu, Lajos AU - Ruzsa, Z. Imre TI - On the equation x(x+d)...(x+(k-1)d)=by2 JF - GLASGOW MATHEMATICAL JOURNAL J2 - GLASGOW MATH J VL - 42 PY - 2000 IS - 2 SP - 255 EP - 261 PG - 7 SN - 0017-0895 DO - 10.1017/S0017089500020115 UR - https://m2.mtmt.hu/api/publication/1093032 ID - 1093032 N1 - Part number: 2 Export Date: 14 May 2021 LA - English DB - MTMT ER - TY - JOUR AU - Pintér, Ákos TI - A note on the Diophantine equation binom{x}{4}=binom{y}{2} JF - PUBLICATIONES MATHEMATICAE DEBRECEN J2 - PUBL MATH DEBRECEN VL - 47 PY - 1995 IS - 3-4 SP - 411 EP - 415 PG - 5 SN - 0033-3883 UR - https://m2.mtmt.hu/api/publication/1111861 ID - 1111861 LA - English DB - MTMT ER -