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Math Help - Getting started on proof with primes! Need guidance

  1. #1
    Junior Member
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    Getting started on proof with primes! Need guidance

    Good day to all,

    I have asked to prove that the following statement is false:

    if p is not prime and p|n^2 then p|n


    My train of thoughts consisted of the following:

    (1) Assume the statement is true and arrive at some contradiction.

    (2) Since p is not prime then it is a composite number and can be expressed uniquely as a product of primes.

    (3) Since we have assumed p|n^2 => n^2 = kp for some integer k

    My problem lies in the fact that I am not quite sure how to merge my assumptions and arrive at some contradiction (if this is even the best method?). As I stated in the title I am not looking for an explicit answer but guidance, as I will learn nothing if someone just hands me the solution.

    Thanks again
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  2. #2
    Junior Member
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    When you're asked to prove that something is false, the best (and in practice, pretty much the only) way to accomplish it is by finding what's called a counter-example, that is, given an implication A\Rightarrow B, you pick an example such that A is satisfied but B is not. In this case, pick for instance p=8 and n=4.
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  3. #3
    Junior Member
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    Thanks Nyrox. I got so wrapped up with my material that even the obvious seems out of reach. Again many thanks...
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