MathLiveEuler's theorem
For positive integers a and n that are coprime, raising a to the power of Euler's totient φ(n) leaves remainder 1 when divided by n. It is used in modular arithmetic, such as simplifying large powers and in RSA cryptography.
a^{\varphi(n)} \equiv 1 \pmod{n}What the symbols mean
| a positive integer coprime to n | |
| a positive integer modulus | |
| Euler's totient function, the count of integers from 1 to n that are coprime to n |
About this formula
- FieldMathematics
- TopicNumber theory
- LevelUniversity
- Also calledFermat–Euler theorem, Euler's totient theorem, Euler theorem modular arithmetic, generalization of Fermat's little theorem, power congruent to 1 modulo n, totient congruence
- SourceWikidata Q193910
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “euler's theorem”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.