Difference between revisions of "Carmichael number"
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==Carmichael numbers== | ==Carmichael numbers== | ||
| − | A [[Carmichael number]] is a [[composite number]]s that satisfies [[Fermat's Little Theorem]]. | + | 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. |
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| + | The first <math>7</math> 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*} | ||
==See Also== | ==See Also== | ||
Revision as of 12:25, 2 August 2022
Carmichael numbers
A Carmichael number is a composite numbers that satisfies Fermat's Little Theorem, 
or 
In this case, 
is the Carmichael number.
The first 
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*}
See Also
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