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Math Help - b is a Zero Divisor ( I think)

  1. #1
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    b is a Zero Divisor ( I think)

    Im new and working on a proof - well actually i cant even start this proof.

    If gcf (n,a) >1 prove there exists b not equal unto 0 mod n but a*b = 0 mod n.
    Im even told that b = n/gcf(n,a)

    any ideas or help will surely be appreciated and allow me to actually spend time with my family instead of staring at this problem for 4 hours getting nowhere.....

    windoze
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  2. #2
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    Re: b is a Zero Divisor ( I think)

    I believe since they give you what b is you can simply substitute n/gcf(n,a) in for b and see if it fulfills those two conditions, which it does.
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Re: b is a Zero Divisor ( I think)

    Quote Originally Posted by windoze View Post
    Im new and working on a proof - well actually i cant even start this proof.

    If gcf (n,a) >1 prove there exists b not equal unto 0 mod n but a*b = 0 mod n.
    Im even told that b = n/gcf(n,a)

    any ideas or help will surely be appreciated and allow me to actually spend time with my family instead of staring at this problem for 4 hours getting nowhere.....

    windoze
    Let gcd (n, a) = x > 1

    Then, n = n1*x and a = a1*x

    Clearly we can pick b = n1 because a*b = a1*x*n1 = a1*n = 0 (mod n)
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