Lucas-Carmichael Number/Examples/935

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Example of Lucas-Carmichael Number

$935$ is a Lucas-Carmichael number:

$p \divides 935 \implies \paren {p + 1} \divides 936$


Proof

We have that:

$935 = 5 \times 11 \times 17$

Then:

\(\ds 936\) \(=\) \(\ds 6 \times 156\) so $\paren {5 + 1} \divides \paren {935 + 1}$
\(\ds \) \(=\) \(\ds 12 \times 78\) so $\paren {11 + 1} \divides \paren {935 + 1}$
\(\ds \) \(=\) \(\ds 18 \times 52\) so $\paren {17 + 1} \divides \paren {935 + 1}$

$\blacksquare$