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 $\paren {19 + 1} \divides \paren {399 + 1}$

$\blacksquare$