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  3. Formalized Mathematics
  4. Formalized Mathematics, 2013, Volume 21, Issue 2

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3679
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    Pole DCWartośćJęzyk
    dc.contributor.authorGrabowski, Adam-
    dc.date.accessioned2015-12-09T20:39:34Z-
    dc.date.available2015-12-09T20:39:34Z-
    dc.date.issued2013-
    dc.identifier.citationFormalized Mathematics, Volume 21, Issue 2, 2013, Pages 103-113-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3679-
    dc.description.abstractIn the article the formal characterization of triangular numbers (famous from [15] and words “EYPHKA! num = Δ+Δ+Δ”) [17] is given. Our primary aim was to formalize one of the items (#42) from Wiedijk’s Top 100 Mathematical Theorems list [33], namely that the sequence of sums of reciprocals of triangular numbers converges to 2. This Mizar representation was written in 2007. As the Mizar language evolved and attributes with arguments were implemented, we decided to extend these lines and we characterized polygonal numbers. We formalized centered polygonal numbers, the connection between triangular and square numbers, and also some equalities involving Mersenne primes and perfect numbers. We gave also explicit formula to obtain from the polygonal number its ordinal index. Also selected congruences modulo 10 were enumerated. Our work basically covers the Wikipedia item for triangular numbers and the Online Encyclopedia of Integer Sequences (http://oeis.org/A000217). An interesting related result [16] could be the proof of Lagrange’s four-square theorem or Fermat’s polygonal number theorem [32].-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.subjecttriangular number-
    dc.subjectpolygonal number-
    dc.subjectreciprocals of triangular numbers-
    dc.titlePolygonal Numbers-
    dc.typeArticle-
    dc.identifier.doi10.2478/forma-2013-0012-
    dc.description.AffiliationInstitute of Informatics University of Białystok Akademicka 2, 15-267 Białystok Poland-
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    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2013, Volume 21, Issue 2

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