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Math Help - Set of numbers

  1. #1
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    Set of numbers

    It is known that the number 2^{13-1} is prime.

    Is n=2^{17-16}

    With all the natural numbers, the number of divisors of n is:

    a) 6
    b) 10
    c) 5
    d) 8
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    It is known that the number 2^{13-1} is prime.

    Is n=2^{17-16}
    ?? 2^{17-16}= 2^1= 2. Did you mean 2^{17-1}?

    With all the natural numbers, the number of divisors of n is:

    a) 6
    b) 10
    c) 5
    d) 8
    ??Is n still [tex]2^{17- 16}? And what does "with all the natural numbers" mean?
    Last edited by HallsofIvy; March 21st 2009 at 04:19 AM.
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  3. #3
    Super Member Showcase_22's Avatar
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    Is 2^{13-1} prime?

    2^{13-1}=2^{12} which is divisible by 2.

    Do you mean 2^{13}-1?

    Do you also mean something like this:

    2^{17}-16=2^{17}-2^4=2^4(2^{13}-1)

    Hence it's divisible by 10 numbers: 2,2^2,2^3,2^4, 2^{13}-1 and 2^{13}-1 multiplied by 2,2^2 and 2^3 AND itself and 1 (forgot those two first time round :s).
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Showcase_22 View Post
    Is 2^{13-1} prime?

    2^{13-1}=2^{12} which is divisible by 2.

    Do you mean 2^{13}-1?

    Do you also mean something like this:

    2^{17}-16=2^{17}-2^4=2^4(2^{13}-1)

    Hence it's divisible by 10 numbers: 2,2^2,2^3,2^4, 2^{13}-1 and 2^{13}-1 multiplied by 2,2^2 and 2^3 AND itself and 1 (forgot those two first time round :s).

    I was trying to figure out how 2^{12} could possibly be prime.
    I had a nasty injection today and I thought maybe my mind was affected by it.
    Whew
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