← Topic 2 · Number Theory
AMC 10/12 · Cheatsheet

Topic 2 · Number Theory

Chapter 4 · AMC 12 · 1% problems

📋 Reference · always available
Order definition
ordn(a)=min⁡{k≥1:ak≡1(modn)}\text{ord}_n(a) = \min\{k \ge 1 : a^k \equiv 1 \pmod n\}
Lagrange bound
ordn(a)∣ϕ(n)\text{ord}_n(a) \mid \phi(n)
Power reduction
ak≡ak mod ordn(a)(modn)a^k \equiv a^{k \bmod \text{ord}_n(a)} \pmod n
Primitive root
Element of order ϕ(n)\phi(n); exists mod every prime pp.