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Mersenne numbers as a difference of two Lucas numbers

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dc.contributor.authorAlan, Murat
dc.date.accessioned2026-06-27T14:47:57Z
dc.date.issued2022
dc.description.abstractLet (L-n)(n >= 0) be the Lucas sequence. We show that the Diophantine equation L-n - L-m = M-k has only the nonnegative integer solutions (n, m, k) = (2, 0, 1), (3, 1, 2), (3, 2, 1), (4, 3, 2), (5, 3, 3), (6, 2, 4), (6, 5, 3) where M-k = 2(k) - 1 is the kth Mersenne number and n > m.en
dc.description.urihttps://doi.org/10.14712/1213-7243.2022.027
dc.identifier.doi10.14712/1213-7243.2022.027
dc.identifier.eissn1213-7243
dc.identifier.endpage276
dc.identifier.issn0010-2628
dc.identifier.issue3
dc.identifier.startpage269
dc.identifier.urihttps://hdl.handle.net/20.500.14981/64915
dc.identifier.volume63
dc.identifier.wos000921727200001
dc.language.isoeng
dc.publisherCHARLES UNIV, FAC MATHEMATICS & PHYSICS
dc.relation.ispartofCOMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE
dc.rightsopenAccess
dc.subjectLucas number
dc.subjectMersenne number
dc.subjectDiophantine equation
dc.subjectlinear forms in logarithm
dc.subjectEQUATION F-N
dc.subjectNONNEGATIVE INTEGER SOLUTIONS
dc.subjectMathematics
dc.titleMersenne numbers as a difference of two Lucas numbers
dc.typeArticle
dspace.entity.typePublication
local.import.sourceWOS

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