已知数列{an}、{bn}满足a1=b1=6,a2=b2=4,a3=b3=3,且{an+1-an}(n∈Z)是等差数列,{bn-2}(n∈Z)是等比数列.
(1)求数列{bn}的通项公式;
(2)求数列{an}的通项公式;
(3)是否存在k∈Z+,使ak-bk∈(0,