Least primitive root
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Definition
Suppose is a natural number such that the multiplicative group modulo
is cyclic (i.e.,
is either a prime number, or
, or a power of an odd prime, or twice the power of an odd prime). The least primitive root or smallest primitive root modulo
is the smallest natural number
such that
is a primitive root modulo
.
Particular cases
Here, we only list equal to a prime or the square of a prime. For something that is a higher power of an odd prime, the smallest primitive root modulo the square of the prime works.
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Smallest primitive root modulo ![]() |
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2 | 1 |
3 | 2 |
4 | 3 |
5 | 2 |
7 | 3 |
11 | 2 |
13 | 2 |
17 | 3 |