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A natural number p is a prime number provided that the only integers dividing p are...

A natural number p is a prime number provided that the only integers dividing
p are 1 and p itself. In fact, for p to be a prime number, it is the same as requiring that
“For all integers x and y, if p divides xy, then p divides x or p divides y.”
Use this property to show that

“If p is a prime number, then √p is an irrational number.”

Please write down a formal proof.

Math   Advanced-Math   
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