Given s,t are non-zero integers, (x,y) is an integer pair , A transformation is to change pair (x,y) into pair (x+t,yās) . If the two integers in a certain pair becoems relatively prime after several tranfomations , then we call the original integer pair "a good pair" .
(1) Is (s,t) a good pair ?
(2) Prove :for any s and t , there exists pair (x,y) which is " a good pair". number theorygreatest common divisorrelatively primenumber theory proposed