(a) Write where .

Sinceadivides bothkand ,adividesr. Similarlybdividesrbecause it divides bothkand .

So and . As is the least positive integer divisible by bothaandband ,rcannot be positive. , i.e. .

(b) First show that if , then . Then note that for any positive integerk, and .

2(a) If , then . Hence since is divisible by 3 for all non-negative integersr.

(b)