Difference between revisions of "Carmichael number"

Revision as of 17:19, 2 August 2022

Carmichael numbers

A Carmichael number is a composite number 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 $7$ Carmichael numbers are:

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

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 ==Carmichael numbers==
-A [[Carmichael number]] is a [[composite number]]s that satisfies [[Fermat's Little Theorem]], <math>a^p \equiv a \pmod{p}.</math>or <math>a^{p - 1} \equiv 1 \pmod{p}.</math> In this case, <math>p</math> is the Carmichael number.
+A [[Carmichael number]] is a [[composite number]] that satisfies [[Fermat's Little Theorem]], <math>a^p \equiv a \pmod{p}.</math>or <math>a^{p - 1} \equiv 1 \pmod{p}.</math> In this case, <math>p</math> is the Carmichael number.
 The first <math>7</math> Carmichael numbers are:

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Difference between revisions of "Carmichael number"

Revision as of 17:19, 2 August 2022

Carmichael numbers

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