Give the Proof of Euclid's decision lemma
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In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely:[note 1]
Euclid's lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b.
For example, if p = 19, a = 133, b = 143, then ab = 133 × 143 = 19019, and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well. In fact, 133 = 19 × 7.
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