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Smallest primitive root

Let n is a natural number greater than 1 and a is an integer such that gcd(a,n)=1. The order of a modulo n, denoted ord_n(a), is the smallest positive integer k such that a^k≡1(mod n)

It is always true that ord_n(a)|ϕ(n). But if additionally ord_n(a)=ϕ(n), where ϕ(n) is the value of Euler's totient function, then a is primitive root. The smallest element of the set of primitive roots is the smallest primitive root

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