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Math Help - Direct proof for the following

  1. #1
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    Direct proof for the following

    Suppose a, b, d, x, and y are integers. Prove that if d|a and d|b then d|(ax+by).

    Pf: Since d|a and d|b then there exists two integers m and n such that dm = a and dn = b.
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  2. #2
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    Quote Originally Posted by algebrapro18 View Post
    Suppose a, b, d, x, and y are integers. Prove that if d|a and d|b then d|(ax+by).

    Pf: Since d|a and d|b then there exists two integers m and n such that dm = a and dn = b.
    d|a means there is an A so that a=dA. d|b means there is a B so that b=dB. Now ax+by = dAx + dBy = d(Ax+By) and so d|(ax+by).
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  3. #3
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    Wow I can't believe I didn't see that...so easy. The reason I asked this is because my professor made it sound MUCH harder than this.
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