Though the proof of this is done in a previous question, I have some doubt about a certain concept. So I ask to clarify it.
In the proof we say that √p=ab (In their lowest form).
Now
p=a2/b2p⋅b2=a2.
Hence p divides a2 so p divides a. We say that the above mentioned condition ("Hence p divides a2 so p divides a") is valid as p is a prime number. I didn't get the fact that why this is only true for prime numbers. Could someone please me this?
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