Euler’s Theorem
An integer that is relatively prime to the modulus, and its power has a periodic structure in the modular sense.
symbols, variables and units
a,n: integer; φ(n): the number of positive integers from 1 to n that are relatively prime to n.
applicable conditions and boundaries
n>1 and gcd(a,n)=1; does not apply to non-coprime cases.
formula source code
The following is a copyable LaTeX expression.
a^{\varphi(n)}\equiv1\pmod nReference and Extended Learning
OpenStax · Algebra and Trigonometry ↗is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.
Euler theoremmodular operationnumber theory