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- Znxc3xa1ms_problem abstract "In number theory, Znám's problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám's problem is named after the Slovak mathematician Štefan Znám, who suggested it in 1972, although other mathematicians had considered similar problems around the same time. One closely related problem drops the assumption of properness of the divisor, and will be called the improper Znám problem hereafter.One solution to the improper Znám problem is easily provided for any k: the first k terms of Sylvester's sequence have the required property. Sun (1983) showed that there is at least one solution to the (proper) Znám problem for each k ≥ 5. Sun's solution is based on a recurrence similar to that for Sylvester's sequence, but with a different set of initial values.The Znám problem is closely related to Egyptian fractions. It is known that there are only finitely many solutions for any fixed k. It is unknown whether there are any solutions to Znám's problem using only odd numbers, and there remain several other open questions.".
- Znxc3xa1ms_problem thumbnail Znam-2-3-11-23-31.svg?width=300.
- Znxc3xa1ms_problem wikiPageExternalLink ZnamProbSols.html.
- Znxc3xa1ms_problem wikiPageExternalLink 1102689567.
- Znxc3xa1ms_problem wikiPageExternalLink home.html.
- Znxc3xa1ms_problem wikiPageExternalLink DESW_dcfs.ps.
- Znxc3xa1ms_problem wikiPageID "1452979".
- Znxc3xa1ms_problem wikiPageLength "11007".
- Znxc3xa1ms_problem wikiPageOutDegree "30".
- Znxc3xa1ms_problem wikiPageRevisionID "632911983".
- Znxc3xa1ms_problem wikiPageWikiLink 18_(number).
- Znxc3xa1ms_problem wikiPageWikiLink 2_(number).
- Znxc3xa1ms_problem wikiPageWikiLink 5_(number).
- Znxc3xa1ms_problem wikiPageWikiLink 96_(number).
- Znxc3xa1ms_problem wikiPageWikiLink Canadian_Mathematical_Bulletin.
- Znxc3xa1ms_problem wikiPageWikiLink Category:Egyptian_fractions.
- Znxc3xa1ms_problem wikiPageWikiLink Category:Integer_sequences.
- Znxc3xa1ms_problem wikiPageWikiLink Category:Mathematical_problems.
- Znxc3xa1ms_problem wikiPageWikiLink Category:Number_theory.
- Znxc3xa1ms_problem wikiPageWikiLink Divisor.
- Znxc3xa1ms_problem wikiPageWikiLink Egyptian_fraction.
- Znxc3xa1ms_problem wikiPageWikiLink Egyptian_fractions.
- Znxc3xa1ms_problem wikiPageWikiLink Journal_of_Number_Theory.
- Znxc3xa1ms_problem wikiPageWikiLink Mathematical_singularity.
- Znxc3xa1ms_problem wikiPageWikiLink Mathematics_Magazine.
- Znxc3xa1ms_problem wikiPageWikiLink Mathematics_of_Computation.
- Znxc3xa1ms_problem wikiPageWikiLink Nondeterministic_finite_automata.
- Znxc3xa1ms_problem wikiPageWikiLink Nondeterministic_finite_automaton.
- Znxc3xa1ms_problem wikiPageWikiLink Number_theory.
- Znxc3xa1ms_problem wikiPageWikiLink Pacific_Journal_of_Mathematics.
- Znxc3xa1ms_problem wikiPageWikiLink Primary_pseudoperfect_number.
- Znxc3xa1ms_problem wikiPageWikiLink Prime_number.
- Znxc3xa1ms_problem wikiPageWikiLink Proper_divisor.
- Znxc3xa1ms_problem wikiPageWikiLink Singularity_(mathematics).
- Znxc3xa1ms_problem wikiPageWikiLink Sylvesters_sequence.
- Znxc3xa1ms_problem wikiPageWikiLink Topology.
- Znxc3xa1ms_problem wikiPageWikiLink Unit_fraction.
- Znxc3xa1ms_problem wikiPageWikiLink Unit_fractions.
- Znxc3xa1ms_problem wikiPageWikiLink Štefan_Znám.
- Znxc3xa1ms_problem wikiPageWikiLink File:Znam-2-3-11-23-31.svg.
- Znxc3xa1ms_problem wikiPageWikiLinkText "Znám's problem".
- Znxc3xa1ms_problem hasPhotoCollection Znxc3xa1ms_problem.
- Znxc3xa1ms_problem title "Znám's Problem".
- Znxc3xa1ms_problem urlname "ZnamsProblem".
- Znxc3xa1ms_problem wikiPageUsesTemplate Template:Citation.
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- Znxc3xa1ms_problem subject Category:Egyptian_fractions.
- Znxc3xa1ms_problem subject Category:Integer_sequences.
- Znxc3xa1ms_problem subject Category:Mathematical_problems.
- Znxc3xa1ms_problem subject Category:Number_theory.
- Znxc3xa1ms_problem comment "In number theory, Znám's problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám's problem is named after the Slovak mathematician Štefan Znám, who suggested it in 1972, although other mathematicians had considered similar problems around the same time.".
- Znxc3xa1ms_problem label "Znám's problem".
- Znxc3xa1ms_problem sameAs Problema_de_Znám.
- Znxc3xa1ms_problem sameAs Problema_de_Znám.
- Znxc3xa1ms_problem sameAs Znám-probléma.
- Znxc3xa1ms_problem sameAs m.052s1z.
- Znxc3xa1ms_problem sameAs Q649322.
- Znxc3xa1ms_problem sameAs Q649322.
- Znxc3xa1ms_problem wasDerivedFrom Znxc3xa1ms_problemoldid=632911983.
- Znxc3xa1ms_problem depiction Znam-2-3-11-23-31.svg.
- Znxc3xa1ms_problem isPrimaryTopicOf Znxc3xa1ms_problem.