Difference between revisions of "Carmichael number"
Enderramsby (talk | contribs) m |
Enderramsby (talk | contribs) m |
||
| (12 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
==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
This article is a stub. Help us out by expanding it.
