Difference between revisions of "Fermat's Little Theorem"

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 x^p − x is an integer multiple of x.

Alternatively, x^p ≡ x (mod p).

Stated another way:

if p is prime and b < p, than b^(p-1) = 1 (mod p).

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 '''[[Fermat]]'s Little Theorem''' (so called to distinguish it from [[Fermat's Last Theorem]]) is that:
-:if p is prime and b < p, than b<sup>(p-1)</sup> = 1(mod 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]]