Problem

NT-B2-M03-P006 Order Criterion

#6 Grade 8 Grade 9 Grade 10 ★★★☆☆ Level 3 of 5

Let \( \gcd(a,m)=1 \) and \(d=\operatorname{ord}_m(a)\). Prove that \(a^k\equiv1\pmod m\) if and only if \(d\mid k\).