prove that if p divides a² than p divides a where a is the positive integer and p is a prime numbers
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If a is some integer then using the Fundamental Theorem of Arithmetic like you mentioned a can be written as a product of prime numbers. Let's say a=bcd where b , c and d are prime numbers. From this we can see that a2=bbccdd. If p divides evenly into a2 then p must be equal to either one of
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