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Let G and H be linear recurrence sequences and let F(x) = dxq + dpxp + dp−1xp−1 + · · · + d0, where d and di ’s are rational integers, be a polynomial. In this paper we showed that for the equation GnHm = F(x), with some restriction, there are no solutions in n, m and x if q > q0, where q0 is an effectively computable positive constant. © 2018, Eszterhazy Karoly College. All rights reserved.
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<div class="JournalArticle Publication short-list"> <div class="authors"> <span class="author-name" mtid="10011731"> <a href="/gui2/?type=authors&mode=browse&sel=10011731" target="_blank">Liptai, Kálmán</a> </span> <span class="author-type"> </span> </div ><div class="title"><a href="/gui2/?mode=browse¶ms=publication;2135423" mtid="2135423" target="_blank">On polynomial values of the product of the terms of linear recurrence sequences</a></div> <div class="pub-info"> <span class="journal-title">ACTA ACADEMIAE PAEDAGOGICAE AGRIENSIS SECTIO MATEMATICAE / AZ ESZTERHÁZY KÁROLY FŐISKOLA TUDOMÁNYOS KÖZLEMÉNYEI. TANULMÁNYOK A MATEMATIKAI TUDOMÁNYOK KÖRÉBŐL</span> <span class="journal-volume">26</span> <span class="page"> pp. 19-23. , 5 p. </span> <span class="year">(1999)</span> </div> <div class="pub-end"><div class="identifier-list"> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:black" title="85042124068" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042124068"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="http://emis.matem.unam.mx/journals/AMI/1999/acta1999-liptai.pdf" target="_blank" href="http://emis.matem.unam.mx/journals/AMI/1999/acta1999-liptai.pdf"> Teljes dokumentum </a> </span> </span> </div> <div class="short-pub-prop-list"> <span class="short-pub-mtid"> Publication:2135423 </span> <span class="status-holder"><span class="status-data status-APPROVED"> Published </span></span> <span class="pub-core">Core </span> <span class="pub-type">Journal Article (Article ) </span> <!-- && !record.category.scientific --> <span class="pub-category">Scientific</span> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 1</span> | Independent citation: 0 | Self citation: 1 | Unknown citation: 0 | Number of citations in Scopus: 1 | WoS/Scopus assigned: 1 </div> </div> </div> </div><div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011731"><a href="/gui2/?type=authors&mode=browse&sel=10011731" target="_blank">Liptai Kálmán (<span class="authorship-author-name">Liptai Kálmán</span> <span class="authorAux-mtmt"> Számelmélet</span>) </a> </span> <span class="author-affil"><span title="Eszterházy Károly Főiskola">EKF</span>/<span title="Faculty of Natural Sciences">FNS</span>/<span title="Institute of Mathematics and Informatics">IMI</span>/Department of Applied Mathematics</span> </div> </div> <div class="title"><a href="/gui2/?mode=browse¶ms=publication;2135423" target="_blank">On polynomial values of the product of the terms of linear recurrence sequences</a></div> <div> <span class="journal-title">ACTA ACADEMIAE PAEDAGOGICAE AGRIENSIS SECTIO MATEMATICAE / AZ ESZTERHÁZY KÁROLY FŐISKOLA TUDOMÁNYOS KÖZLEMÉNYEI. TANULMÁNYOK A MATEMATIKAI TUDOMÁNYOK KÖRÉBŐL</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1589-6498">1589-6498</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1216-6014">1216-6014</a>)</span>: <span class="journal-volume">26</span> <span class="page"> pp 19-23 </span> <span class="year">(1999)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Language: English | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:black" title="85042124068" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042124068"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="http://emis.matem.unam.mx/journals/AMI/1999/acta1999-liptai.pdf" target="_blank" href="http://emis.matem.unam.mx/journals/AMI/1999/acta1999-liptai.pdf"> Teljes dokumentum </a> </span> </span> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 1</span> | Independent citation: 0 | Self citation: 1 | Unknown citation: 0 | Number of citations in Scopus: 1 | WoS/Scopus assigned: 1 </div> <div class="mtid"><span class="long-pub-mtid">Publication: 2135423</span> | <span class="status-data status-APPROVED"> Published </span> <span class="oldId">Old id: 2135423</span> | Core | <span class="type-subtype">Journal Article ( Article ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Last Modified: 2023.10.09. 13:35 Krisztina Oszlánczi (EKE admin) </div> </div></div>
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<div class="BookChapter Publication short-list"> <div class="authors"> <span class="author-name" > Brindza, B </span> <span class="author-type"> </span> ; <span class="author-name" mtid="10011731"> <a href="/gui2/?type=authors&mode=browse&sel=10011731" target="_blank">Liptai, K</a> </span> <span class="author-type"> </span> ; <span class="author-name" mtid="10011723"> <a href="/gui2/?type=authors&mode=browse&sel=10011723" target="_blank">Szalay, L</a> </span> <span class="author-type"> </span> </div ><div class="title"><a href="/gui2/?mode=browse¶ms=publication;1805904" mtid="1805904" target="_blank">On products of the terms of linear recurrences</a></div> <div class="InBook">In: Győry, K; Pethő, A; Sós, VT (eds.) <span class="booktitle"><a href="/gui2/?mode=browse¶ms=publication;167444" target="_blank">Number Theory: Diophantine, Computational and Algebraic Aspects : Proceedings of the Intenational Conference held in Eger, Hungary, July 29 - August 2, 1996 </a></span > </div><div class="pub-info"> <span class="publishedAt">New York City, United States of America,</span> <span class="publishedAt">Berlin, Germany : <span class="publisher">Walter de Gruyter GmbH & Co KG</span> <span class="year">(1998)</span> <span class="pageLength">613 p.</span> <span class="page"> pp. 101-106. , 6 p. </span> </div> <div class="pub-end"><div class="identifier-list"> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:black" title="10.1515/9783110809794.101" target="_blank" href="https://doi.org/10.1515/9783110809794.101"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="Zbl 0909.11003" target="_blank" href="https://zbmath.org/?q=an%3AZbl 0909.11003"> Zentralblatt für Mathematik </a> </span> </span> </div> <div class="short-pub-prop-list"> <span class="short-pub-mtid"> Publication:1805904 </span> <span class="status-holder"><span class="status-data status-ADMIN_APPROVED"> Admin approved </span></span> <span class="pub-core">Core </span> <span class="pub-type">Chapter in Book (Study ) </span> <!-- && !record.category.scientific --> <span class="pub-category">Scientific</span> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 14</span> | Independent citation: 13 | Self citation: 1 | Unknown citation: 0 | Number of citations in WoS: 4 | Number of citations in Scopus: 2 | WoS/Scopus assigned: 5 | Number of citations with DOI: 4 </div> </div> </div> </div><div class="BookChapter Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <div class="autype autype0"> <span class="author-name" >Brindza B </span> ; <span class="author-name" mtid="10011731"><a href="/gui2/?type=authors&mode=browse&sel=10011731" target="_blank">Liptai K (<span class="authorship-author-name">Liptai Kálmán</span> <span class="authorAux-mtmt"> Számelmélet</span>) </a> </span> <span class="author-affil"><span title="Eszterházy Károly Főiskola">EKF</span>/<span title="Faculty of Natural Sciences">FNS</span>/<span title="Institute of Mathematics and Informatics">IMI</span>/Department of Applied Mathematics</span> ; <span class="author-name" mtid="10011723"><a href="/gui2/?type=authors&mode=browse&sel=10011723" target="_blank">Szalay L (<span class="authorship-author-name">Szalay László</span> <span class="authorAux-mtmt"> Számelmélet</span>) </a> </span> <span class="author-affil"><span title="University of West Hungary">UWH</span>/<span title="Erdőmérnöki Kar">EMK</span>/Institute of Mathematics</span> </div> </div> <div class="title"><a href="/gui2/?mode=browse¶ms=publication;1805904" target="_blank">On products of the terms of linear recurrences</a></div> <div class="InBook"><div class="chapter-in">In:</div> <div class="authors"> <div class="autype autype-1"> <span class="author-name" mtid="10000953"><a href="/gui2/?type=authors&mode=browse&sel=10000953" target="_blank">Győry K (<span class="authorship-author-name">Győry Kálmán</span> <span class="authorAux-mtmt"> Matematika, számelmélet</span>) </a> </span> <span class="author-affil"><span title="Office for Research Groups Attached to Universities and Other Institutions of the Hungarian Academy of Sciences">MTA TKI</span>/MTA-DE Számelméleti Kutatócsoport</span> ; <span class="author-name" mtid="10000413"><a href="/gui2/?type=authors&mode=browse&sel=10000413" target="_blank">Pethő A (<span class="authorship-author-name">Pethő Attila</span> <span class="authorAux-mtmt"> Számelmélet</span>) </a> </span> <span class="author-affil"><span title="University of Debrecen">UD</span>/Faculty of Informatics</span> ; <span class="author-name" mtid="10000936"><a href="/gui2/?type=authors&mode=browse&sel=10000936" target="_blank">Sós VT (<span class="authorship-author-name">T. 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<div class="JournalArticle Publication short-list"> <div class="authors"> <span class="author-name" mtid="10011723"> <a href="/gui2/?type=authors&mode=browse&sel=10011723" target="_blank">Szalay, L</a> </span> <span class="author-type"> </span> </div ><div class="title"><a href="/gui2/?mode=browse¶ms=publication;1805834" mtid="1805834" target="_blank">A note on the products of the terms of linear recurrences</a></div> <div class="pub-info"> <span class="journal-title">ACTA ACADEMIAE PAEDAGOGICAE AGRIENSIS SECTIO MATEMATICAE / AZ ESZTERHÁZY KÁROLY FŐISKOLA TUDOMÁNYOS KÖZLEMÉNYEI. TANULMÁNYOK A MATEMATIKAI TUDOMÁNYOK KÖRÉBŐL</span> <span class="journal-volume">24</span> <span class="page"> pp. 47-53. , 7 p. </span> <span class="year">(1997)</span> </div> <div class="pub-end"><div class="identifier-list"> <span class="identifiers"> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="320" target="_blank" href="http://publicatio.uni-sopron.hu/320/"> SOE Publicatio repozitórium </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="http://ami.ektf.hu/uploads/papers/finalpdf/AAPASM_24_from47to53.pdf" target="_blank" href="http://ami.ektf.hu/uploads/papers/finalpdf/AAPASM_24_from47to53.pdf"> Teljes dokumentum </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="Zbl 0886.11042" target="_blank" href="https://zbmath.org/?q=an%3AZbl 0886.11042"> Zentralblatt für Mathematik </a> </span> </span> </div> <div class="short-pub-prop-list"> <span class="short-pub-mtid"> Publication:1805834 </span> <span class="status-holder"><span class="status-data status-ADMIN_APPROVED"> Admin approved </span></span> <span class="pub-core">Core </span> <span class="pub-type">Journal Article (Article ) </span> <!-- && !record.category.scientific --> <span class="pub-category">Scientific</span> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 8</span> | Independent citation: 8 | Self citation: 0 | Unknown citation: 0 | Number of citations in WoS: 2 | Number of citations in Scopus: 1 | WoS/Scopus assigned: 3 | Number of citations with DOI: 2 </div> </div> </div> </div><div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011723"><a href="/gui2/?type=authors&mode=browse&sel=10011723" target="_blank">Szalay L (<span class="authorship-author-name">Szalay László</span> <span class="authorAux-mtmt"> Számelmélet</span>) </a> </span> <span class="author-affil"><span title="University of West Hungary">UWH</span>/<span title="Erdőmérnöki Kar">EMK</span>/Institute of Mathematics</span> </div> </div> <div class="title"><a href="/gui2/?mode=browse¶ms=publication;1805834" target="_blank">A note on the products of the terms of linear recurrences</a></div> <div> <span class="journal-title">ACTA ACADEMIAE PAEDAGOGICAE AGRIENSIS SECTIO MATEMATICAE / AZ ESZTERHÁZY KÁROLY FŐISKOLA TUDOMÁNYOS KÖZLEMÉNYEI. TANULMÁNYOK A MATEMATIKAI TUDOMÁNYOK KÖRÉBŐL</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1589-6498">1589-6498</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1216-6014">1216-6014</a>)</span>: <span class="journal-volume">24</span> <span class="page"> pp 47-53 </span> <span class="year">(1997)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Language: English | </span> <span class="identifiers"> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="320" target="_blank" href="http://publicatio.uni-sopron.hu/320/"> SOE Publicatio repozitórium </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="http://ami.ektf.hu/uploads/papers/finalpdf/AAPASM_24_from47to53.pdf" target="_blank" href="http://ami.ektf.hu/uploads/papers/finalpdf/AAPASM_24_from47to53.pdf"> Teljes dokumentum </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="Zbl 0886.11042" target="_blank" href="https://zbmath.org/?q=an%3AZbl 0886.11042"> Zentralblatt für Mathematik </a> </span> </span> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 8</span> | Independent citation: 8 | Self citation: 0 | Unknown citation: 0 | Number of citations in WoS: 2 | Number of citations in Scopus: 1 | WoS/Scopus assigned: 3 | Number of citations with DOI: 2 </div> <div class="mtid"><span class="long-pub-mtid">Publication: 1805834</span> | <span class="status-data status-ADMIN_APPROVED"> Admin approved </span> <span class="oldId">Old id: 1805834</span> | Core | <span class="type-subtype">Journal Article ( Article ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Last Modified: 2015.03.28. 16:51 Zsófia Tompáné Székely (SOE admin 4) </div> </div></div>