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 $\paren {17 + 1} \divides \paren {935 + 1}$ |
$\blacksquare$