Diophantine equations concerning various means of binomial coefficients

A tétel rövid nézete
dc.contributor.authorRakamazi, Richárd
dc.date.accessioned2024-09-04T09:47:00Z
dc.date.available2024-09-04T09:47:00Z
dc.date.issued2014-06-01
dc.description.abstractThe main goal of this paper is to show by elementary methods, that there are infinitely many different pairs of binomial coefficients of the form (n C 2) such that also their arithmetic, geometric and harmonic means, resp. have the same form. We give all solutions for the arithmetic mean. We also give infinitely many non-trivial solutions for the arithmetic mean of three binomial coefficients satisfying some special conditions. The proofs require the solution of some other interesting Diophantine equations, too. Since the author is also a secondary school teacher, we use elementary methods that mostly can be discussed in secondary school, mainly within the framework of group study sessions. This explains why the means are generally analysed for two terms and for binomial coefficients with "lower" value 2, since further generalizations require substantially deeper mathematical methods which are beyond the frames of this paper.en
dc.formatapplication/pdf
dc.identifier.citationTeaching Mathematics and Computer Science, Vol. 12 No. 1 (2014) , 71-79
dc.identifier.doihttps://doi.org/10.5485/TMCS.2014.0357
dc.identifier.eissn2676-8364
dc.identifier.issn1589-7389
dc.identifier.issue1
dc.identifier.jatitleTeach. Math. Comp. Sci.
dc.identifier.jtitleTeaching Mathematics and Computer Science
dc.identifier.urihttps://hdl.handle.net/2437/379758
dc.identifier.volume12
dc.languageen
dc.relationhttps://ojs.lib.unideb.hu/tmcs/article/view/14948
dc.rights.accessOpen Access
dc.rights.ownerRichárd Rakamazi
dc.subjectdiophantine equationsen
dc.subjectbinomial coefficientsen
dc.subjectarithmeticen
dc.subjectgeometric and harmonic means of binomial coefficientsen
dc.titleDiophantine equations concerning various means of binomial coefficientsen
dc.typefolyóiratcikkhu
dc.typearticleen
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Teaching Mathematics and Computer Science (DE-journals)