{"id":2003,"date":"2023-12-08T16:19:09","date_gmt":"2023-12-08T16:19:09","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2003"},"modified":"2023-12-11T13:34:47","modified_gmt":"2023-12-11T13:34:47","slug":"on-solutions-of-the-diophantine-equation-pm-%e2%88%92-ln-c","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-solutions-of-the-diophantine-equation-pm-%e2%88%92-ln-c\/","title":{"rendered":"On solutions of the Diophantine equation Pm \u2212 Ln = c"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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On solutions of the Diophantine equation \\mathcal{P}_m \u2212 L_n = c<\/span><\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Pagdame Tiebekabe<\/strong>\\,^{1,2} <\/span> <\/i>, Serge Adonsou\\,^3 <\/span> and Isma\u00efla Diouf \\,^1 <\/span>
\\,^1 <\/span> D\u00e9partement de Math\u00e9matiques et Informatique, Universit\u00e9 Cheikh Anta Diop, Dakar, BP 5005 Dakar-fann, S\u00e9n\u00e9gal.
\\,^2 <\/span> D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Kara, BP 404 Kara – Togo.
\\,^3 <\/span> D\u00e9partement de Math\u00e9matique et Informatique, African Insitute for Mathematical Sciences, 6 Melrose Avenue Cape Town 7945.<\/p>\n\n\n\n

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Pages 246\u2013261 | Received 03 March 2023, Accepted 12 August 2023, Published 11 December 2023 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

In this article, we determine all the integers c having at least two representations as difference between two linear recurrent sequences. This is a variant of the Pillai\u2019s equation. This equation is an exponential Diophantine equation. The proof of our main theorem uses lower bounds for linear forms of logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Linear forms in logarithms, Diophantine equations, Pillai\u2019s problem, Linear recurrent sequences. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 11B39, 11J86; Secondary 11D617.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On solutions of the Diophantine equation Pagdame Tiebekabe , Serge Adonsou and Isma\u00efla Diouf D\u00e9partement de Math\u00e9matiques et Informatique, Universit\u00e9 Cheikh Anta Diop, Dakar, BP 5005 Dakar-fann, S\u00e9n\u00e9gal. D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Kara, BP 404 Kara – Togo. D\u00e9partement de Math\u00e9matique et Informatique, African Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-2003","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=2003"}],"version-history":[{"count":10,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2003\/revisions"}],"predecessor-version":[{"id":2084,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2003\/revisions\/2084"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}