(a) If p is a prime and , prove that in the arithmetic progression
every p th term is divisible by p.
[Hint: Because gcd(p,b)= 1, there exist integers r and s satisfying pr + bs= 1. Put nk = kp − as for k= 1,2,… and show that p|(a + nkb).]
(b) From part (a), conclude that if b is an odd integer, then every other term in the indicated progression is even.
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