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- Cyclic_number_(group_theory) abstract "A cyclic number is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic iff any group of order n is cyclic.Any prime number is clearly cyclic. All cyclic numbers are square-free.Let n = p1 p2 … pk where the pi are distinct primes, then φ(n) = (p1 − 1)(p2 − 1)...(pk – 1). If no pi divides any (pj – 1), then n and φ(n) have no common (prime) divisor, and n is cyclic.The first cyclic numbers are 1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 123, 127, 131, 133, 137, 139, 141, 143, 145, 149, ... (sequence A003277 in OEIS).".
- Cyclic_number_(group_theory) wikiPageID "30495448".
- Cyclic_number_(group_theory) wikiPageLength "1558".
- Cyclic_number_(group_theory) wikiPageOutDegree "10".
- Cyclic_number_(group_theory) wikiPageRevisionID "690758912".
- Cyclic_number_(group_theory) wikiPageWikiLink Category:Number_theory.
- Cyclic_number_(group_theory) wikiPageWikiLink Coprime_integers.
- Cyclic_number_(group_theory) wikiPageWikiLink Cyclic_group.
- Cyclic_number_(group_theory) wikiPageWikiLink Eulers_totient_function.
- Cyclic_number_(group_theory) wikiPageWikiLink Group_(mathematics).
- Cyclic_number_(group_theory) wikiPageWikiLink If_and_only_if.
- Cyclic_number_(group_theory) wikiPageWikiLink Natural_number.
- Cyclic_number_(group_theory) wikiPageWikiLink Order_(group_theory).
- Cyclic_number_(group_theory) wikiPageWikiLink Prime_number.
- Cyclic_number_(group_theory) wikiPageWikiLink Square-free_integer.
- Cyclic_number_(group_theory) wikiPageWikiLinkText "Cyclic number (group theory)".
- Cyclic_number_(group_theory) wikiPageWikiLinkText "cyclic number".
- Cyclic_number_(group_theory) wikiPageWikiLinkText "cyclic".
- Cyclic_number_(group_theory) wikiPageUsesTemplate Template:OEIS.
- Cyclic_number_(group_theory) wikiPageUsesTemplate Template:Reflist.
- Cyclic_number_(group_theory) subject Category:Number_theory.
- Cyclic_number_(group_theory) hypernym Number.
- Cyclic_number_(group_theory) type Field.
- Cyclic_number_(group_theory) comment "A cyclic number is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic iff any group of order n is cyclic.Any prime number is clearly cyclic. All cyclic numbers are square-free.Let n = p1 p2 … pk where the pi are distinct primes, then φ(n) = (p1 − 1)(p2 − 1)...(pk – 1).".
- Cyclic_number_(group_theory) label "Cyclic number (group theory)".
- Cyclic_number_(group_theory) sameAs Q5198222.
- Cyclic_number_(group_theory) sameAs m.0g9xgj_.
- Cyclic_number_(group_theory) sameAs Q5198222.
- Cyclic_number_(group_theory) wasDerivedFrom Cyclic_number_(group_theory)?oldid=690758912.
- Cyclic_number_(group_theory) isPrimaryTopicOf Cyclic_number_(group_theory).