Question In Elementary Number Thoery

In the book, "Elementary Number Theory 6th Edition(David M. Burton)", I don't know how to solve this problem.

P.58 number 18 (a)

If p is a prime and b is not divisible by p, prove that in the

arithmetic progression a, a+b, a+2b, ....
every pth term is divisible by p
(Hint : Because gcd(p, b)=1, there exist integers r and s satisfying pr+bs=1. Put n(k)=kp-as for k = 1,2,3... and show that a+n(k) is divisible by p)

By the above hint, I can result in pl(a+n(k)), but after that, I don't know how to continue this problem. Thank you very much if you give me some help.