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Math Help - Prove divisibility

  1. #1
    mol
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    Prove divisibility

    How to prove that if:
    a + b + c == 0 (mod n)$ and a^5 + b^5 + c^5 == 0 (mod n),
    abc == 0 (mod n) ;/
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Not true!

    1+1+1\equiv 0 \mod 3

    1^5+1^5+1^5\equiv 0 \mod 3

    but 1^3 \not\equiv 0 \mod 3.
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  3. #3
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    Quote Originally Posted by mol View Post
    How to prove that if:
    a + b + c == 0 (mod n)$ and a^5 + b^5 + c^5 == 0 (mod n),
    abc == 0 (mod n) ;/

    This is false: take a=b=c=2\,,\,\, n = 6

    Tonio
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