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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?
I see. Is this theorem helpful in any specific fields of mathematics?
Yes, it is extremely useful in number theory and algebra. It forms the basis for many important results and proofs in these fields.