Glossary¶

coprime¶

Two integers whose only common divisor is 1

primitive root¶

A number \(g\) is a primitive root modulo \(n\) if every number coprime to \(n\) is congruent to a power of \(g \bmod{n}\).

Euler’s totient function¶

Euler’s totient function \(\varphi (n)\) counts the positive integers up to \(n\) that are relatively prime to \(n\)

Carmichael function¶

The Carmichael function \(\lambda (n)\) is the smallest possible integer \(m\) satisfying

\[a ^ m \equiv 1 \bmod{n} \quad \text{for } n\in \mathbb {Z} > 0\]

for every integer \(a\) between 1 and \(n\) that is coprime to \(n\)