Primitive element (finite field)

In field theory, a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field. In other words, ${\displaystyle \alpha \in \mathrm {GF} (q)}$ is called a primitive element if it is a primitive (q−1)th root of unity in GF(q); this means that all the non-zero elements of ${\displaystyle \mathrm {GF} (q)}$ can be written as ${\displaystyle \alpha ^{i}}$ for some (positive) integer ${\displaystyle i}$.

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