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  2. Czasopisma naukowe / Journals
  3. Formalized Mathematics
  4. Formalized Mathematics, 2009, Volume 17, Issue 2

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3527
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    Pole DCWartośćJęzyk
    dc.contributor.authorRiccardi, Marco-
    dc.date.accessioned2015-12-01T19:26:34Z-
    dc.date.available2015-12-01T19:26:34Z-
    dc.date.issued2009-
    dc.identifier.citationFormalized Mathematics, Volume 17, Issue 2, 2009, Pages 123-128-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3527-
    dc.description.abstractThis article formalizes proofs of some elementary theorems of number theory (see [1, 26]): Wilson's theorem (that n is prime iff n > 1 and (n - 1)! ≅ -1 (mod n)), that all primes (1 mod 4) equal the sum of two squares, and two basic theorems of Euclid and Euler about perfect numbers. The article also formally defines Euler's sum of divisors function Φ, proves that Φ is multiplicative and that Σ k|n Φ(k) = n.-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.titleThe Perfect Number Theorem and Wilson's Theorem-
    dc.typeArticle-
    dc.identifier.doi10.2478/v10037-009-0013-y-
    dc.description.AffiliationCasella Postale 49, 54038 Montignoso, Italy-
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    dc.description.referencesArtur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179-186, 2004.-
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    dc.description.referencesTakaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.-
    dc.description.referencesBeata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.-
    dc.description.referencesPiotr Rudnicki. Little Bezout theorem (factor theorem). Formalized Mathematics, 12(1):49-58, 2004.-
    dc.description.referencesPiotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.-
    dc.description.referencesPiotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.-
    dc.description.referencesAndrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.-
    dc.description.referencesAndrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.-
    dc.description.referencesAndrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.-
    dc.description.referencesAndrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.-
    dc.description.referencesMichał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.-
    dc.description.referencesWojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.-
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.-
    dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.-
    dc.description.referencesHiroshi Yamazaki, Yasunari Shidama, and Yatsuka Nakamura. Bessel's inequality. Formalized Mathematics, 11(2):169-173, 2003.-
    Występuje w kolekcji(ach):Formalized Mathematics, 2009, Volume 17, Issue 2

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