Problem

Source: Croatia 1999 1st Grade P4

Tags: number theory



A triple of numbers $(a_1,a_2,a_3)=(3,4,12)$ is given. The following operation is performed a finite number of times: choose two numbers $a,b$ from the triple and replace them by $0.6x-0.8y$ and $0.8x+0.6y$. Is it possible to obtain the (unordered) triple $(2,8,10)$?