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Math Help - Numbers (urgent)

  1. #1
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    Exclamation Numbers (urgent)

    a) determine the remainder when 2^2009+1 is divided by 17

    b) prove that 30^99+61^100 is divisible by 31

    c) it is known that the numbers p and 8p^2+1 are primes. Find p

    thnx a million
    justanotherperson

    PS: if u can include working out that would be great. XD
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by justanotherperson View Post
    a) determine the remainder when 2^2009+1 is divided by 17

    b) prove that 30^99+61^100 is divisible by 31

    c) it is known that the numbers p and 8p^2+1 are primes. Find p

    thnx a million
    justanotherperson

    PS: if u can include working out that would be great. XD
    a) 2^4=-1\ (mod\ 17)

    (2^4)^{502}=(-1)^{502}\ (mod\ 17)

    2^{2008}=1\ (mod\ 17)

    2^{2009}=2\ (mod\ 17)

    2^{2009}+1=3\ (mod\ 17)

    The remainder when 2^{2009}+1 is divided by 17 is 3.

    b) 30^{99}+61^{100}

    =(31-1)^{99}+(62-1)^{100}

    Now expand using binomial theorem. (Note that 62=31*2)
    Last edited by alexmahone; August 10th 2009 at 07:27 AM.
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  3. #3
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