This is a general question regarding divisibility

If $c|a$ and $c|b$, does $c|a+b$?

Where $a,b,c$ are integers

If yes, does this also hold for general rings?

  • 1
    $\begingroup$ If $a = a'c$ and $b = b'c$, then $$a+b = a'c + b'c = (a'+b')c$$ $\endgroup$ – peterwhy Apr 21 at 21:44
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    $\begingroup$ What did you try? Write what $c|a$ and $c|b$ mean by definition, and you will see it is very easy to conclude that $c|a+b$. $\endgroup$ – Mark Apr 21 at 21:45

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