In number theory a Carmichael number is a composite positive integer , which satisfies the congruence for all integers which are relatively prime to . Being relatively prime means that they do not have common divisors, other than 1. Such numbers are named after Robert Carmichael.
All prime numbers satisfy for all integers which are relatively prime to . This has been proven by the famous mathematician Pierre de Fermat. In most cases if a number is composite, it does not satisfy this congruence equation. So, there exist not so many Carmichael numbers. We can say that Carmichael numbers are composite numbers that behave a little bit like they would be a prime number.
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Other polynomial numbers |
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- Hilbert
- Idoneal
- Leyland
- Loeschian
- Lucky numbers of Euler
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- Fibonacci
- Jacobsthal
- Leonardo
- Lucas
- Padovan
- Pell
- Perrin
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Possessing a specific set of other numbers |
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- Congruent
- Knödel
- Riesel
- Sierpiński
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Expressible via specific sums |
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- Nonhypotenuse
- Polite
- Practical
- Primary pseudoperfect
- Ulam
- Wolstenholme
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Figurate numbers |
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2-dimensional | centered |
- Centered triangular
- Centered square
- Centered pentagonal
- Centered hexagonal
- Centered heptagonal
- Centered octagonal
- Centered nonagonal
- Centered decagonal
- Star
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non-centered |
- Triangular
- Square
- Square triangular
- Pentagonal
- Hexagonal
- Heptagonal
- Octagonal
- Nonagonal
- Decagonal
- Dodecagonal
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3-dimensional | centered |
- Centered tetrahedral
- Centered cube
- Centered octahedral
- Centered dodecahedral
- Centered icosahedral
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non-centered |
- Tetrahedral
- Cubic
- Octahedral
- Dodecahedral
- Icosahedral
- Stella octangula
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pyramidal | |
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4-dimensional | non-centered |
- Pentatope
- Squared triangular
- Tesseractic
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Combinatorial numbers |
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- Bell
- Cake
- Catalan
- Dedekind
- Delannoy
- Euler
- Eulerian
- Fuss–Catalan
- Lah
- Lazy caterer's sequence
- Lobb
- Motzkin
- Narayana
- Ordered Bell
- Schröder
- Schröder–Hipparchus
- Stirling first
- Stirling second
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- Wieferich
- Wall–Sun–Sun
- Wolstenholme prime
- Wilson
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Pseudoprimes |
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- Carmichael number
- Catalan pseudoprime
- Elliptic pseudoprime
- Euler pseudoprime
- Euler–Jacobi pseudoprime
- Fermat pseudoprime
- Frobenius pseudoprime
- Lucas pseudoprime
- Lucas–Carmichael number
- Somer–Lucas pseudoprime
- Strong pseudoprime
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Arithmetic functions and dynamics |
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Divisor functions | |
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Prime omega functions | |
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Euler's totient function |
- Highly cototient
- Highly totient
- Noncototient
- Nontotient
- Perfect totient
- Sparsely totient
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Aliquot sequences |
- Amicable
- Perfect
- Sociable
- Untouchable
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Primorial | |
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- Blum
- Cyclic
- Erdős–Nicolas
- Erdős–Woods
- Friendly
- Giuga
- Harmonic divisor
- Lucas–Carmichael
- Pronic
- Regular
- Rough
- Smooth
- Sphenic
- Størmer
- Super-Poulet
- Zeisel
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Arithmetic functions and dynamics | Digit sum |
- Digit sum
- Digital root
- Self
- Sum-product
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Digit product |
- Multiplicative digital root
- Sum-product
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Coding-related | |
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Other |
- Dudeney
- Factorion
- Kaprekar
- Kaprekar's constant
- Keith
- Lychrel
- Narcissistic
- Perfect digit-to-digit invariant
- Perfect digital invariant
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P-adic numbers-related | |
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Digit-composition related |
- Palindromic
- Pandigital
- Repdigit
- Repunit
- Self-descriptive
- Smarandache–Wellin
- Strictly non-palindromic
- Undulating
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Digit-permutation related |
- Cyclic
- Digit-reassembly
- Parasitic
- Primeval
- Transposable
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Divisor-related |
- Equidigital
- Extravagant
- Frugal
- Harshad
- Polydivisible
- Smith
- Vampire
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Other | |
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- Pancake number
- Sorting number
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