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Math Help - Proof relating to prime numbers

  1. #1
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    Proof relating to prime numbers

    Hi

    I need help with this following proof. I can't seem to prove it. I believe there is something relating to coprime in this question.

    I have attached my question as i didn't know all the various commands to type it in latex.

    thanks
    Attached Thumbnails Attached Thumbnails Proof relating to prime numbers-question-prime-numbers.gif  
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rpatel View Post
    Hi

    I need help with this following proof. I can't seem to prove it. I believe there is something relating to coprime in this question.

    I have attached my question as i didn't know all the various commands to type it in latex.

    thanks
    What have you tried? I suppose you cannot use the FTA.
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  3. #3
    Moo
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    Quote Originally Posted by Drexel28 View Post
    What have you tried? I suppose you cannot use the FTA.
    How would you use the FTA here ?

    Well, the proof of the FTA uses methods that may be useful here :P



    Edit : sorry, I've been constantly editing my message. This is the final version
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Moo View Post
    What's the relationship between his question and the fundamental theorem of algebra ?
    Well, it's kind of cheating since you need this result to prove the FTA. Since p|ab we know that ab=p\cdot p_1\cdots p_m and since a and b must be written as a product of those primes it follows that p must be in one of them. That's roughly the cheat.
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    what does FTA stand for ?
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rpatel View Post
    what does FTA stand for ?
    Fundamental theorem of arithmetic.
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  7. #7
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    oh ok i haven't come accross FTA before.
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