Difference between revisions of "Carmichael number"

Line 6: Line 6:
  
 
\begin{align}
 
\begin{align}
561 = & 3 \cdot 11 \cdot 17 \\
+
561 &= 3 \cdot 11 \cdot 17 \\
1105 = & 5 \cdot 13 \cdot 17 \\
+
1105 &= 5 \cdot 13 \cdot 17 \\
1729 = & 7 \cdot 13 \cdot 19 \\
+
1729 &= 7 \cdot 13 \cdot 19 \\
2465 = & 5 \cdot 17 \cdot 29 \\
+
2465 &= 5 \cdot 17 \cdot 29 \\
2821 = & 7 \cdot 13 \cdot 31 \\
+
2821 &= 7 \cdot 13 \cdot 31 \\
6601 = & 7 \cdot 23 \cdot 41 \\
+
6601 &= 7 \cdot 23 \cdot 41 \\
8991 = & 7 \cdot 19 \cdot 67
+
8991 &= 7 \cdot 19 \cdot 67.
 
\end{align}
 
\end{align}
  

Revision as of 12:28, 2 August 2022

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}

See Also

~ User:Enderramsby


This article is a stub. Help us out by expanding it.