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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?
Can you give me an example of how this theorem works?
Sure. Let's say that [math]p = 5[/math], [math]a = 20[/math], and [math]b = 3[/math]. We know that [math]p[/math] divides the product [math]ab = 60[/math]. Since [math]5[/math] is a prime that does not divide [math]3[/math], it must divide [math]a[/math], which is [math]20[/math].