Answer with Step-by-step explanation:
Since we have given that
a + b = c
and a|c
i.e. a divides c.
We need to prove that a|b.
⇒ a = mb for some integer m
Since a|c,
So, mathematically, it is expressed as
c= ka
Now, we put the above value in a + b = c.
So, it becomes,
[tex]a+b=c\\\\a+b=ka\\\\b=ka-a\\\\b=a(k-1)\\\\\implies a|b[/tex]
a=mb, here, m = k-1
Hence, proved.
