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- Carmichael's_theorem abstract "This article refers to Carmichael's theorem about Fibonacci numbers. Carmichael's theorem may also refer to the recursive definition of the Carmichael function.Carmichael's theorem, named after the American mathematician R.D. Carmichael, states that for n greater than 12, the nth Fibonacci number F(n) has at least one prime divisor that does not divide any earlier Fibonacci number. The only exceptions for n up to 12 are:F(1)=1 and F(2)=1, which have no prime divisorsF(6)=8 whose only prime divisor is 2 (which is F(3))F(12)=144 whose only prime divisors are 2 (which is F(3)) and 3 (which is F(4))If a prime p is a divisor of F(n) that does not divide any F(m) with m < n, then p is called a characteristic factor or a primitive prime divisor of F(n). Carmichael's theorem says that every Fibonacci number, apart from the exceptions listed above, has at least one primitive prime divisor.The theorem can be generalized from Fibonacci numbers to other Lucas sequences.".
- Carmichael's_theorem wikiPageExternalLink yabuta.pdf.
- Carmichael's_theorem wikiPageExternalLink fib.html.
- Carmichael's_theorem wikiPageExternalLink primefactor.
- Carmichael's_theorem wikiPageID "932711".
- Carmichael's_theorem wikiPageRevisionID "543504251".
- Carmichael's_theorem hasPhotoCollection Carmichael's_theorem.
- Carmichael's_theorem subject Category:Fibonacci_numbers.
- Carmichael's_theorem subject Category:Theorems_in_number_theory.
- Carmichael's_theorem type Abstraction100002137.
- Carmichael's_theorem type Amount105107765.
- Carmichael's_theorem type Attribute100024264.
- Carmichael's_theorem type Communication100033020.
- Carmichael's_theorem type FibonacciNumbers.
- Carmichael's_theorem type Magnitude105090441.
- Carmichael's_theorem type Message106598915.
- Carmichael's_theorem type Number105121418.
- Carmichael's_theorem type Property104916342.
- Carmichael's_theorem type Proposition106750804.
- Carmichael's_theorem type Statement106722453.
- Carmichael's_theorem type Theorem106752293.
- Carmichael's_theorem type TheoremsInNumberTheory.
- Carmichael's_theorem comment "This article refers to Carmichael's theorem about Fibonacci numbers. Carmichael's theorem may also refer to the recursive definition of the Carmichael function.Carmichael's theorem, named after the American mathematician R.D. Carmichael, states that for n greater than 12, the nth Fibonacci number F(n) has at least one prime divisor that does not divide any earlier Fibonacci number.".
- Carmichael's_theorem label "Carmichael's theorem".
- Carmichael's_theorem label "Teorema de Carmichael".
- Carmichael's_theorem label "Teorema di Carmichael".
- Carmichael's_theorem sameAs Teorema_de_Carmichael.
- Carmichael's_theorem sameAs Teorema_di_Carmichael.
- Carmichael's_theorem sameAs m.03r7k5.
- Carmichael's_theorem sameAs Q3889376.
- Carmichael's_theorem sameAs Q3889376.
- Carmichael's_theorem sameAs Carmichael's_theorem.
- Carmichael's_theorem wasDerivedFrom Carmichael's_theorem?oldid=543504251.
- Carmichael's_theorem isPrimaryTopicOf Carmichael's_theorem.