In Carl Friedrich Gauss's treatise "Disquisitiones Arithmeticae", the statement of the lemma is Euclid's Proposition 14 (Section 2), which he uses to prove the uniqueness of the decomposition product of prime factors of an integer (Theorem 16), admitting the existence as "obvious." From this existence and uniqueness he then deduces the generalization of prime numbers to integers. For this reason, the generalization of Euclid's lemma is sometimes referred to as Gauss's lemma, but some believe this usage is incorrect due to confusion with Gauss's lemma on quadratic residues.