Carmichael number

Carmichael numbers

A Carmichael number is a composite numbers that satisfies Fermat's Little Theorem, $a^p \equiv a \pmod{p}.$ or $a^{p - 1} \equiv 1 \pmod{p}.$ In this case, $p$ is the Carmichael number.

The first $7$ are:

$\begin{align} 561 &= 3 \cdot 11 \cdot 17 \\ 1105 &= 5 \cdot 13 \cdot 17 \\ 1729 &= 7 \cdot 13 \cdot 19 \\ 2465 &= 5 \cdot 17 \cdot 29 \\ 2821 &= 7 \cdot 13 \cdot 31 \\ 6601 &= 7 \cdot 23 \cdot 41 \\ 8991 &= 7 \cdot 19 \cdot 67. \end{align}$

Page

Toolbox

Search

Carmichael number

Carmichael numbers

See Also