# Divisor Properties

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?

• If $a = a'c$ and $b = b'c$, then $$a+b = a'c + b'c = (a'+b')c$$ – peterwhy Apr 21 at 21:44
• 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 $c|a+b$. – Mark Apr 21 at 21:45