- #1

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A prime number

*p*is a factor of a non-zero product of integers a*b if and only if it is a facotr of a and/or b.

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- Thread starter liangiecar
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- #1

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A prime number

- #2

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The "if" direction is obvious. For the "only if", you need to use the fundamental theorem of arithmetic. Because a*b has a unique prime decomposition, if a prime p divides a*b then it must be one of the primes in the decomposition. The prime decomposition of a*b is just the product of the decompositions of a and b, so p must divide a and/or b.

This sounds like a homework question! In which case you will need to be a lot more rigorous when you write it out.

This sounds like a homework question! In which case you will need to be a lot more rigorous when you write it out.

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- #3

CompuChip

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For the converse implication, the easiest way I can think of is using the unique decomposition of any integer into its prime factors.

- #4

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thx,guys

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