@article{MTMT:1138460, title = {Perfect powers from products of consecutive terms in arithmetic progression}, url = {https://m2.mtmt.hu/api/publication/1138460}, author = {Győry, Kálmán and Hajdu, Lajos and Pintér, Ákos}, doi = {10.1112/S0010437X09004114}, journal-iso = {COMPOS MATH}, journal = {COMPOSITIO MATHEMATICA}, volume = {145}, unique-id = {1138460}, issn = {0010-437X}, year = {2009}, eissn = {1570-5846}, pages = {845-864} } @article{MTMT:1105972, title = {Arithmetic progressions of squares, cubes and n-th powers}, url = {https://m2.mtmt.hu/api/publication/1105972}, author = {Hajdu, Lajos and Tengely, Szabolcs}, doi = {10.7169/facm/1261157805}, journal-iso = {FUNCT APPROX COMMENT MATH}, journal = {FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI}, volume = {41}, unique-id = {1105972}, issn = {0208-6573}, abstract = {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.}, year = {2009}, eissn = {2080-9433}, pages = {129-138} } @article{MTMT:1105971, title = {Cubes in products of terms in arithmetic progression}, url = {https://m2.mtmt.hu/api/publication/1105971}, author = {Hajdu, Lajos and Tijdeman, R and Tengely, Szabolcs}, journal-iso = {PUBL MATH DEBRECEN}, journal = {PUBLICATIONES MATHEMATICAE DEBRECEN}, volume = {74}, unique-id = {1105971}, issn = {0033-3883}, year = {2009}, eissn = {2064-2849}, pages = {215-232} } @article{MTMT:1098342, title = {Powers from products of consecutive terms in arithmetic progression}, url = {https://m2.mtmt.hu/api/publication/1098342}, author = {Bennett, MA and Bruin, N and Győry, Kálmán and Hajdu, Lajos}, doi = {10.1112/S0024611505015625}, journal-iso = {P LOND MATH SOC}, journal = {PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY}, volume = {92}, unique-id = {1098342}, issn = {0024-6115}, year = {2006}, eissn = {1460-244X}, pages = {273-306} } @article{MTMT:1073987, title = {Arithmetic progressions consisting of unlike powers}, url = {https://m2.mtmt.hu/api/publication/1073987}, author = {Bruin, N and Győry, Kálmán and Hajdu, Lajos and Tengely, Szabolcs}, doi = {10.1016/S0019-3577(07)00002-X}, journal-iso = {INDAGAT MATH NEW SER}, journal = {INDAGATIONES MATHEMATICAE-NEW SERIES}, volume = {17}, unique-id = {1073987}, issn = {0019-3577}, abstract = {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.}, year = {2006}, eissn = {1872-6100}, pages = {539-555} } @article{MTMT:1092759, title = {On the diophantine equation n(n+d)...(n+(k-1)d)=by^l}, url = {https://m2.mtmt.hu/api/publication/1092759}, author = {Győry, Kálmán and Hajdu, Lajos and Saradha, N}, doi = {10.4153/CMB-2004-037-1}, journal-iso = {CAN MATH BULL}, journal = {CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES}, volume = {47}, unique-id = {1092759}, issn = {0008-4395}, year = {2004}, eissn = {1496-4287}, pages = {373-388} } @article{MTMT:1242196, title = {Perfect powers in arithmetic progression. A note on the inhomogeneous case}, url = {https://m2.mtmt.hu/api/publication/1242196}, author = {Hajdu, Lajos}, doi = {10.4064/aa113-4-4}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {113}, unique-id = {1242196}, issn = {0065-1036}, year = {2004}, eissn = {1730-6264}, pages = {343-349} } @article{MTMT:1242125, title = {The resolution of the diophantine equation x(x+d)...(x+(k-1)d)=by^2 for fixed d}, url = {https://m2.mtmt.hu/api/publication/1242125}, author = {Filakovszky, P and Hajdu, Lajos}, doi = {10.4064/aa98-2-5}, journal-iso = {ACTA ARITH}, journal = {ACTA ARITHMETICA}, volume = {98}, unique-id = {1242125}, issn = {0065-1036}, year = {2001}, eissn = {1730-6264}, pages = {151-154} } @article{MTMT:1093032, title = {On the equation x(x+d)...(x+(k-1)d)=by2}, url = {https://m2.mtmt.hu/api/publication/1093032}, author = {Brindza, B and Hajdu, Lajos and Ruzsa, Z. Imre}, doi = {10.1017/S0017089500020115}, journal-iso = {GLASGOW MATH J}, journal = {GLASGOW MATHEMATICAL JOURNAL}, volume = {42}, unique-id = {1093032}, issn = {0017-0895}, year = {2000}, eissn = {1469-509X}, pages = {255-261} } @article{MTMT:1111861, title = {A note on the Diophantine equation binom{x}{4}=binom{y}{2}}, url = {https://m2.mtmt.hu/api/publication/1111861}, author = {Pintér, Ákos}, journal-iso = {PUBL MATH DEBRECEN}, journal = {PUBLICATIONES MATHEMATICAE DEBRECEN}, volume = {47}, unique-id = {1111861}, issn = {0033-3883}, year = {1995}, eissn = {2064-2849}, pages = {411-415} }