Fermat's little theorem
If p is prime and a is not a multiple of p, then leaves remainder 1 when divided by p. History: 1640.
How to work it out
- 1
The statement:
- 2
If p is prime and a is not a multiple of p, then leaves remainder 1 when divided by p.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ a^{p-1} \equiv 1 \pmod p \]mod 7 for a = 1 to 6 (computed)
| a | aā¶ | aā¶ mod 7 |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 64 | 1 |
| 3 | 729 | 1 |
| 4 | 4096 | 1 |
| 5 | 15625 | 1 |
| 6 | 46656 | 1 |
Questions
What is the fermat's little theorem?
If p is prime and a is not a multiple of p, then leaves remainder 1 when divided by p.
Who is the Fermat's little theorem associated with?
Pierre de Fermat.