Noun
Carmichael number (plural Carmichael numbers)
(mathematics) A composite number
n
{\displaystyle n}
that satisfies the modular arithmetic congruence relation
b
n
−
1
≡
1
(
mod
n
)
{\displaystyle b^{n-1}\equiv 1{\pmod {n}}}
for all integers
1
<
b
<
n
{\displaystyle 1
Carmichael number (plural Carmichael numbers)
(mathematics) A composite number
n
{\displaystyle n}
that satisfies the modular arithmetic congruence relation
b
n
−
1
≡
1
(
mod
n
)
{\displaystyle b^{n-1}\equiv 1{\pmod {n}}}
for all integers
1
<
b
<
n
{\displaystyle 1
that are relatively prime to
n
{\displaystyle n}
.
A heuristic argument, given in the same paper, appears to suggest that there are infinitely many Carmichael numbers of order m, for any m. However, not a single Carmichael number of order 3 or above is known. Source: Internet
Alternately, any number p satisfying the equality : is either a prime or a Carmichael number. Source: Internet
An order 2 Carmichael number According to Howe, 17 · 31 · 41 · 43 · 89 · 97 · 167 · 331 is an order 2 Carmichael number. Source: Internet
In 1910, Carmichael citation found the first and smallest such number, 561, which explains the name "Carmichael number". Source: Internet
The number is a Carmichael number if its three factors are all prime. Source: Internet