p was supposed to stand for prime... And no, no questions anymore.Ok so I finally watched the KhanAcademy video, and it has the proof that if p is a prime that divides ##b^2##, then p divides ##b##. You just incorrectly generalized it to all integer p.
With that explained, can you repeat what was your original question? Do you have trouble understanding the reasoning in the video? You aren't looking for all p for which the proof is valid, are you?