Fermat's Little Theorem/Examples/5 Divides 8^4-1

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
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