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High Quality Content by WIKIPEDIA articles! In modular arithmetic, a branch of number theory, a primitive root modulo n is any number g with the property that any number coprime to n is congruent to a power of g. Gauss defines primitive root in Article 57 of the Disquisitiones Arithmeticae, where he credits Euler with coining the term. In Art. 56 he states that Lambert and Euler knew of them, but that his is the first rigorous demonstration that they exist. In fact, the Disquisitiones has two proofs: the one in Art. 54 is a nonconstructive existence proof, the one in Art. 55 is constructive.