if $a|c$ and $a+b=c$ prove that $a|b$

Question

I started of doing this $a|c$ implies $c=am$ where $m$ is some integer

But then I don’t know what to do after I know that it is true but I can’t prove it can someone please help me

Is "$a/c$" meant to be "$a$ divides $c$"? If so, you should use the vertical bar |, not the slash. — Arturo Magidin, Jan 27 '20 at 19:52
What's the difference between this question and your previous one? — Andrew Chin, Jan 27 '20 at 19:57
Given that from $a+b=c$ we can get $a+(-c)=-b$, and questions of divisibility are not affected by a minus sign, they are in fact the same question. — Arturo Magidin, Jan 27 '20 at 20:17

score 0 · Answer 1 · answered Jan 27 '20 at 19:52

0

Say $a|c$. That means $c=am$.

If $b=c-a$, then $b=am-a=a(m-1),$ so $ a$ divides $b$ too.

answered Jan 27 '20 at 19:52

J. W. Tanner

1 Answers1