The conversation between human and AI assistant.
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?
Can you explain to me the meaning of the theorem: "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]"?
Yes, I can. This theorem is known as the Fundamental Theorem of Arithmetic. It states that if a prime number divides the product of two integers, then it must divide at least one of the integers.