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Bot GPT 3.5 If alc and b|c, then we know that c is divisible by b, which means c = kb for some integer k.
We also know that alc, which means a is a multiple of c.
So, we can write a = mc, where m is an integer.
Now, let's substitute these values into (a + b) c:
(a + b) c = (mc + b) (kb)
= (mkb + b) (kb)
= (mk + 1) kb
= k(mk + 1) b
Since mk + 1 is an integer (as m and k are integers), we can rewrite this as:
k(mk + 1) b = k' b
Therefore, we have shown that (a + b) c is divisible by b, confirming the statement (a + b) c if alc and b|c.