Proof! Prove statement about divisiblity?

Question

Prove the statement about the divisibility of integers

If d I (a+b), and d I a, then d I b

Answer 1

We can use the distributive property of the division with respect to the sum.

(a +b)/d = a/d + b/d. By assumption, it follows (a + b)/d and a/d are integers, which implies so is b/d. Therefore, d|b.

Answer 2

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Answer 3

I would suggest that you learn to ask questions in a recognizable form. What is that crap you wrote??
and the answerer before me knows that 37239=sajkdfj he is smarter than both of us!!

Answer 4

d|(a+b) ⇔ ∃c: cd=(a+b)
d|a ⇔ ∃k: kd=a

Then if d|(a+b) and d|a, then cd = a+b = kd + b, so b = (c-k)d, which means that d|b. Q.E.D.