Difference between revisions of "Carmichael number"
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==Carmichael numbers== | ==Carmichael numbers== | ||
− | A [[Carmichael number]] is a [[composite 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: | ||
+ | |||
+ | <cmath>\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}</cmath> | ||
==See Also== | ==See Also== | ||
* [[Fermat's Little Theorem]] | * [[Fermat's Little Theorem]] | ||
+ | * [[Carmichael function]] | ||
+ | |||
− | ~ [[User:Enderramsby]] | + | ~ [[User:Enderramsby|enderramsby]] |
{{stub}} | {{stub}} | ||
− | [[Category:Number | + | [[Category:Number theory]] |
Latest revision as of 14:52, 3 August 2022
Carmichael numbers
A Carmichael number is a composite number that satisfies Fermat's Little Theorem, or In this case, is the Carmichael number.
The first Carmichael numbers are:
See Also
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