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Math Help - Mod Question

  1. #1
    Junior Member
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    Oct 2008
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    Mod Question

    Show that 5^n + 6^n = 0 mod 11, for all odd number n

    My initial attempt was to prove by induction. Base case is obvious, and the induction step would be to prove for n + 2.

    I'm trying to play around by writing in the mod definition but no luck so far. Any advice?
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  2. #2
    MHF Contributor
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    Re: Mod Question

    Quote Originally Posted by hashshashin715 View Post
    Show that 5^n + 6^n = 0 mod 11, for all odd number n

    My initial attempt was to prove by induction. Base case is obvious, and the induction step would be to prove for n + 2.

    I'm trying to play around by writing in the mod definition but no luck so far. Any advice?
    You want to show that IF

    5^k+6^k is divisible by 11

    THEN

    5^{k+2}+6^{k+2}

    will also be divisible by 11.

    So

    5^{k+2}+6^{k+2}=(25)5^k+(36)6^k=(22)5^k+(33)6^k+3 \left(5^k+6^k\right)
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  3. #3
    Junior Member
    Joined
    Oct 2008
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    Re: Mod Question

    Thanks a lot, i got it now.

    I was getting stuck at the part where we have (25)5^k + (36)5^k. Breaking them down like that was clever.
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