Proof Pearl: Bounding Least Common Multiples with Triangles

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dc.contributor.authorChan, Hing Lun Joseph
dc.contributor.authorNorrish, Michael
dc.date.accessioned2021-09-06T00:06:00Z
dc.date.issued2017
dc.date.updated2023-01-15T07:17:37Z
dc.description.abstractWe present a proof of the fact that Open image in new window for \(n \ge 0\). This result has a standard proof via an integral, but our proof is purely number-theoretic, requiring little more than inductions based on lists. The almost-pictorial proof is based on manipulations of a variant of Leibniz’s harmonic triangle, itself a relative of Pascal’s better-known Triangle.
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn0168-7433en_AU
dc.identifier.urihttp://hdl.handle.net/1885/247360
dc.language.isoen_AUen_AU
dc.publisherKluwer Academic Publishers
dc.rights© Springer Science+Business Media B.V. 2017
dc.sourceJournal of Automated Reasoning
dc.subjectLeast common multiple
dc.subjectPascal’s triangle
dc.subjectLeibniz’s triangle
dc.subjectFormalisation
dc.subjectAutomated theorem proving
dc.subjectHOL4
dc.subjectBinomial coefficients
dc.titleProof Pearl: Bounding Least Common Multiples with Triangles
dc.typeJournal article
local.bibliographicCitation.lastpage22en_AU
local.bibliographicCitation.startpage1en_AU
local.contributor.affiliationChan, Hing Lun Joseph, College of Engineering and Computer Science, ANUen_AU
local.contributor.affiliationNorrish, Michael, College of Engineering and Computer Science, ANUen_AU
local.contributor.authoremailu4988135@anu.edu.auen_AU
local.contributor.authoruidChan, Hing Lun Joseph, u4988135en_AU
local.contributor.authoruidNorrish, Michael, u4087502en_AU
local.description.embargo2099-12-31
local.description.notesImported from ARIESen_AU
local.identifier.absfor019999 - Mathematical Sciences not elsewhere classifieden_AU
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciencesen_AU
local.identifier.ariespublicationu4351680xPUB351en_AU
local.identifier.doi10.1007/s10817-017-9438-0en_AU
local.identifier.scopusID2-s2.0-85031406482
local.identifier.thomsonIDWOS:000458119500002
local.identifier.uidSubmittedByu4351680en_AU
local.publisher.urlhttps://www.springernature.com/gp/products/journalsen_AU
local.type.statusPublished Versionen_AU

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