(a) Use the Euclidean Algorithm to nd gcd (2017; 271) and use this to nd integers x and y so that gcd(2017; 271) = 2017x + 271y.

Question

(b) Is it true that for all integers a and b, if not both a and b are zeros then not both 5a+3band3a+2barezeros,andgcd(5a+3b;3a+2b)=gcd(a;b)? Proveyouranswer. (c) Is it true that for all integers a and b, if not both a and b are zeros then not both 3a+4band3a+2barezeros,andgcd(3a+4b;3a+2b)=gcd(a;b)? Proveyouranswer.