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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, … (sequence A003277 in OEIS).".
- Cyclic_number_(group_theory) wikiPageID "30495448".
- Cyclic_number_(group_theory) wikiPageRevisionID "568192644".
- Cyclic_number_(group_theory) hasPhotoCollection Cyclic_number_(group_theory).
- Cyclic_number_(group_theory) subject Category:Number_theory.
- 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 m.0g9xgj_.
- Cyclic_number_(group_theory) sameAs Q5198222.
- Cyclic_number_(group_theory) sameAs Q5198222.
- Cyclic_number_(group_theory) wasDerivedFrom Cyclic_number_(group_theory)?oldid=568192644.
- Cyclic_number_(group_theory) isPrimaryTopicOf Cyclic_number_(group_theory).