Suppose $a$, $b$, and $c$ are integers. Prove that if $a \mid b$ and $a \mid c$, then $a \mid (b +c)$
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Do you mean $a\mid b$? – Rick Sep 06 '15 at 15:50
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1Use the definition of $\mid$ – Hagen von Eitzen Sep 06 '15 at 15:52
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yes you are right – Garo Jeriar Bozadjian Sep 06 '15 at 15:53
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Have you attempted the proof yourself? Please include any work you have done and indicate where you are stuck so that you receive responses that address the specific difficulties you are encountering. – N. F. Taussig Sep 06 '15 at 16:16
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if $a|b$ and $a|c$ then exist integers $m,n$ with $b=ma$ and $c=na$ now we compute $b+c=am+an=a(m+n)$ and from here we get $a|(b+c)$ per definition.
Dr. Sonnhard Graubner
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