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Math Help - mod questions

  1. #1
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    mod questions

    Show that 5^e +6^e is congruent 0 (mod 11) for all odd numbers e





    Prove that 6(4^n) is congruent 6(mod 9) for any n>=0
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  2. #2
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    x^n + y^n = (x+y)(x^{n-1}-x^{n-2}y+x^{n-3}y^2-...) where n is odd.
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  3. #3
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by ashe2203 View Post

    Prove that 6(4^n) is congruent 6(mod 9) for any n>=0
    for n=0, we have 6(4^0) \equiv 6\mod 9
    for for n=1, we have 6(4^1) \equiv 24\mod 9 \equiv 6\mod 9
    for suppose it is true that for n=k, 6(4^k) \equiv 6\mod 9..
    then, 6(4^{k+1}) = 6(4^k)(4) \equiv (6)(4)\mod 9 \equiv 24\mod 9 \equiv 6\mod 9.. QED.
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