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Math Help - Math Proof Help

  1. #1
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    Math Proof Help

    Hi, this is my first time posting.

    The problem was to prove that the only prime of the form (n^5)-1 is 31.

    My plan is to first write that there is another prime of that form and then somehow prove that that prime is the same prime in the above problem, 31.

    But I'm not sure how to get there, some help please?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Is...

    n^{5}-1 = (n-1)\cdot (n^{4}+n^{3}+n^{2} + n +1) (1)

    ... then n^{5} -1 is prime only if n-1=1, i.e. n=2. The primes of the type 2^{k} -1 are known as 'Mersenne primes'...



    Merry Christmas from Italy

    \chi \sigma
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  3. #3
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    Quote Originally Posted by ivinew View Post
    Hi, this is my first time posting.

    The problem was to prove that the only prime of the form (n^5)-1 is 31.

    My plan is to first write that there is another prime of that form and then somehow prove that that prime is the same prime in the above problem, 31.

    But I'm not sure how to get there, some help please?
    31^5-1=2\times 3 \times 5^2 \times 11 \times 17351

    CB
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  4. #4
    Senior Member Shanks's Avatar
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    I think, chisigma is quite right!
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  5. #5
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    chisigma!!! Thanks sooo muchh!!!

    I see it now~
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  6. #6
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    Quote Originally Posted by CaptainBlack View Post
    31^5-1=2\times 3 \times 5^2 \times 11 \times 17351

    CB
    I don't understand. What does 35^5- 1 have to do with n^5- 1= 31?
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by HallsofIvy View Post
    I don't understand. What does 35^5- 1 have to do with n^5- 1= 31?
    nothing I misread the question

    CB
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  8. #8
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    You mean I'm not the only one who does that?
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  9. #9
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    Quote Originally Posted by HallsofIvy View Post
    You mean I'm not the only one who does that?
    Me too
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