MathDB
GOOD pair

Source: 1998 HK

January 5, 2012
number theorygreatest common divisorrelatively primenumber theory proposed

Problem Statement

Given s,ts,t are non-zero integers, (x,y)(x,y) is an integer pair , A transformation is to change pair (x,y)(x,y) into pair (x+t,yāˆ’s)(x+t,y-s) . 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)(s,t) a good pair ? (2) Prove :for any ss and tt , there exists pair (x,y)(x,y) which is " a good pair".
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