Htykuut

up vote 1 down vote favorite Here's what my textbook asks me to prove: From algebra, recall that, if a prime $p$ divides a product $ab$ , then $p$ must divide either $a$ or $b$ . Use this to prove that $sqrt{p}$ is irrational for any prime $p$ . I know the proof follows exactly like the proof of irrationality of $sqrt{2}$ . But my question is, what if $b=a$ ? Then the statement would follow like "if $p$ divides $a^2$ then either $p$ divides $a$ or $p$ divides $a$ " which is false. I wonder if I am doing some mistake here because the following video https://youtu.be/uQ6KSt94jVY seems to prove the same statement. I think it should be an "inclusive or" there. logic share | cite | i