Answer:
Proof for [tex]k|r[/tex]
Step-by-step explanation:
We are given that a, n, b, r and k are integers.
Also,
[tex]a = nb + r[/tex]
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 [tex]k|r[/tex]
Putting value of a and b in the equation, we get:
[tex]rk = n(sk) + r\\r = rk - nsk\\r = (r-sn)k[/tex]
Since, (r-sn) is an integer, k divides r.
