A={a|1≤a≤2000,a=4k+1,k∈Z}
={1,5,9,13,17,21,25,29,...}
B={b|1≤b≤3000,b=3k-1,k∈Z}
={2,5,8,11,14,17,20,23,...}
A∩B={5,17,29,...}
3,4的最小公倍數(shù)是12
所以A∩B的元素差值都是12的倍數(shù)
故A∩B={5,17,29,...,1997}
共有167個
所以|A∩B|=167