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Primitive root modulo n facts for kids

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In modular arithmetic, a number g is a primitive root modulo n, if every number m from 1..(n-1) can be expressed in the form of g^x\equiv m \pmod n. As an example, 3 is a primitive root modulo 7:

3^1 \equiv 3\ \pmod 7
3^2 \equiv 2\ \pmod 7
3^3 \equiv 6\ \pmod 7
3^4 \equiv 4\ \pmod 7
3^5 \equiv 5\ \pmod 7
3^6 \equiv 1\ \pmod 7

All the elements 1, 2, \ldots, 6 of the group modulo 7 can be expressed that way. The number 2 is no primitive root modulo 7, because

2^3=8 \equiv 1 \pmod 7

and

2^6=64 \equiv 1 \pmod 7

See also

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