Question

If aſc and a +b = C, prove that a|b.

Answer 1

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,

$a+b=c\\\\a+b=ka\\\\b=ka-a\\\\b=a(k-1)\\\\\implies a|b$

a=mb, here, m = k-1

Hence, proved.