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• 20:11, 23 January 2022 Beijayl talk contribs created page If a prime divides a product it divides one of the factors (Created page with "'''If a prime <math>p</math> divides a product <math>ab</math> it also divides either <math>a</math> or <math>b</math>''', also called '''Euclid's lemma''', is a classic result in number theory. ==Proof== Suppose <math>p</math> divides <math>ab</math> but doesn't divide <math>b</math>. Then <math>p</math> and <math>b</math> are co-prime, so their greatest common divisor is one. Bézout's lemma ensures that there are integers <math>x\text{, }y</math> such that <math>p...")