Lucas-Carmichael Number/Examples/399
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Example of Lucas-Carmichael Number
$399$ is a Lucas-Carmichael number:
- $p \divides 399 \implies \paren {p + 1} \divides 400$
Proof
We have that:
- $399 = 3 \times 7 \times 19$
Then:
\(\ds 400\) | \(=\) | \(\ds 4 \times 100\) | so $\paren {3 + 1} \divides \paren {399 + 1}$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 8 \times 100\) | so $\paren {7 + 1} \divides \paren {399 + 1}$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 20 \times 20\) | so $\paren {19 + 1} \divides \paren {399 + 1}$ |
$\blacksquare$