Fermat's little theorem

For any integer a and prime p, raising a to the power p gives a result congruent to a modulo p. It is used in number theory, primality testing, and modular arithmetic.

a^{p} \equiv a \pmod{p}

What the symbols mean

any integer
a prime number

About this formula

  • FieldMathematics
  • TopicNumber theory
  • LevelUniversity
  • Also calledfermat's theorem prime power congruence, modular exponentiation prime, Fermat's theorem number theory
  • SourceWikidata Q188295

Write it in Obsidian

MathLive is a free visual math editor for Obsidian. Run Find a formula, type “fermat's little theorem”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.

Related formulas