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Math Help - Number Theory Congruences Proof

  1. #1
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    Number Theory Congruences Proof

    Hey I'm not really sure how to start out this problem.

    We have to prove that if a = b (mod n), then ac = bc (mod n)

    How exactly would I prove from a=b to ac = bc for this problem?
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    Hello,
    Quote Originally Posted by BlakeRobertsonMD View Post
    Hey I'm not really sure how to start out this problem.

    We have to prove that if a = b (mod n), then ac = bc (mod n)

    How exactly would I prove from a=b to ac = bc for this problem?
    You can go to the definition of the congruence :

    a=b (mod n) <===> there exists an integer k (positive or negative) such that a-b = kn

    so from that, if you multiply by c : ac-bc=kcn. Let k'=cn.
    Then ac-bc=k'n <===> ac=bc (mod n)
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