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In page Finite field:

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In a finite field of order q {\displaystyle q} , the polynomial X q − X {\displaystyle X^{q}-X} has all q {\displaystyle q} elements of the finite field as roots.[citation needed] The non-zero elements of a finite field form a multiplicative group. This group is cyclic, so all non-zero elements can be expressed as powers of a single element called a primitive element of the field. (In general there will be several primitive elements for a given field.)[1]