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Math Help - proof and intergers

  1. #1
    Junior Member
    Joined
    Nov 2009
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    29

    proof and intergers

    Hi,

    Does anyone know how to solve this one :

    let a, b, c Z ( integer set ) with a|b and a|c , show that for any m , n Z , a|mb+nc
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  2. #2
    Member Black's Avatar
    Joined
    Nov 2009
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    If a|b then there's a k_1 \in \mathbb{Z} s.t k_1a=b. If a|c then there's a k_2 \in \mathbb{Z} s.t k_2a=c.

    For any m,n \in \mathbb{Z}, mb+nc=m(k_1a)+n(k_2a)=(mk_1+nk_2)a \Rightarrow a|mb+nc.
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