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When [math]p[/math] is a prime and [math]a, b[/math] are integers, [math](p \mid ab) \Rightarrow (p \mid a) \lor (p \mid b)[/math]. What is the meaning of this theorem?
How does this theorem relate to prime factorization?
The theorem is actually a consequence of the prime factorization theorem. It can be proved using the fact that any integer greater than 1 can be uniquely expressed as a product of primes.