Difference between revisions of "Fermat's Little Theorem"
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| − | [[Fermat]]'s Little Theorem is | + | '''[[Fermat]]'s Little Theorem''' (so called to distinguish it from [[Fermat's Last Theorem]]) is that: |
| − | :if p is prime and b < p, | + | : if p is a [[prime number]], then for any integer x, the number x<sup>p</sup> − x is an integer multiple of x. |
| − | [[ | + | |
| + | :Alternatively, x<sup>p</sup> ≡ x (mod p). | ||
| + | |||
| + | Stated another way: | ||
| + | :if p is prime and b < p, than b<sup>(p-1)</sup> = 1 (mod p). | ||
| + | |||
| + | [[Category:Mathematics]] | ||
| + | [[Category:Number Theory]] | ||
Latest revision as of 23:46, May 28, 2025
Fermat's Little Theorem (so called to distinguish it from Fermat's Last Theorem) is that:
- if p is a prime number, then for any integer x, the number xp − x is an integer multiple of x.
- Alternatively, xp ≡ x (mod p).
Stated another way:
- if p is prime and b < p, than b(p-1) = 1 (mod p).