Fermat's Little Theorem/Examples/5 Divides 8^4-1
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Examples of Use of Fermat's Little Theorem
- $5 \divides 8^4 - 1$
where $\divides$ denotes divisibility.
Proof
| \(\ds 8^4\) | \(=\) | \(\ds 4096\) | ||||||||||||
| \(\ds \leadsto \ \ \) | \(\ds 8^4 - 1\) | \(=\) | \(\ds 4095\) | |||||||||||
| \(\ds \) | \(=\) | \(\ds 5 \times 819\) |
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Fermat's theorem
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Fermat's theorem