Lucas-Carmichael Number/Examples/2915
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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 $\paren {31 + 1} \divides \paren {2915 + 1}$ |
$\blacksquare$