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Math Help - primes and unique factorization

  1. #16
    Senior Member Dinkydoe's Avatar
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    ok..i understand where you're coming from now. so since p / b^2 it also divides b..
    indeed. I hope you understood the steps leading upto p|b^2.

    The definition of prime-numbers say: if p|mn \Rightarrow p|m or p|n

    Apply that idea to p|b\cdot b then follows that p|b.
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  2. #17
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    yes..i do..understand how we got where we did..

    for b, your saying counter-example, as in prove it is tru by saying that if p does not divide a^2 + b^2 then it does not divide a^2 + b^2 nor c^2 + d^2.
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  3. #18
    Senior Member Dinkydoe's Avatar
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    No. It means you're giving an example that shows the given statement is false.

    A statement like: For all n we have n+1 = 5 is clearly false. Then n= 1 is an counterexample against that statement.
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  4. #19
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    ok.. i think i see where you're coming from
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  5. #20
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    Are you sure that a is false..if p divides thoroughly isnt the statement tru?
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  6. #21
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    so that would make a and b false then..correct..
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  7. #22
    Senior Member Dinkydoe's Avatar
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    (a) and (b) is false. For (a) I gave you a counterexample in the first post. For (b) try to come up with a counter-example yourself.

    (c) correct.
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