Let a, n, b, r, and k be integers. if a = nb+r and k|a and k|b, then k|r

Proof for

Step-by-step explanation:

We are given that a, n, b, r and k are integers.

Also,

Since k divides a and b, we can write,

a = rk and b = sk, where r and s are integers.

Now, we have to prove that k divides r as well that is

Putting value of a and b in the equation, we get:

Since, (r-sn) is an integer, k divides r.

1 1/7 hope i

step-by-step explanation:

8/7 = (1 * 7 + 1) / 7 = 1 + 1/7 = 1 1/7

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x