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Let p be a prime and let a and b be relatively prime integers. Prove that if p2

Chapter 7, Problem 20

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QUESTION:

Let p be a prime and let a and b be relatively prime integers. Prove that if p2 | ab, then p2 | a or p2 | b.

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QUESTION:

Let p be a prime and let a and b be relatively prime integers. Prove that if p2 | ab, then p2 | a or p2 | b.

ANSWER:

Step 1 of 2

Let  and  be integers with  .

If  and  , then         ....(1)

Let,

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