Lucas-Carmichael Number/Examples/2915

From ProofWiki
Jump to navigation Jump to search

Example of Lucas-Carmichael Number

$2915$ is a Lucas-Carmichael number:

$p \divides 2915 \implies \paren {p + 1} \divides 2916$


Proof

We have that:

$2915 = 5 \times 11 \times 53$

Then:

\(\ds 2916\) \(=\) \(\ds 6 \times 486\) so $\paren {5 + 1} \divides \paren {2915 + 1}$
\(\ds \) \(=\) \(\ds 12 \times 243\) so $\paren {13 + 1} \divides \paren {2915 + 1}$
\(\ds \) \(=\) \(\ds 54 \times 54\) so $\paren {31 + 1} \divides \paren {2915 + 1}$

$\blacksquare$