(a-b)^2013=1
a²-a+(2b+1)²+1/4=0
a²-a+4b²+4b+1+1/4=0
(2a)²-4a+(4b)²+16b+5=0
(2a)²-2×2a×1+1+(4b)²+2×4b×2+2²=0
(2a-1)²+(4b+2)²=0
因为：(2a-1)²≥0,(4b+2)²≥0
所以,有：(2a-1)²=0,(4b+2)²=0
解得：a=1/2、b=-1/2
(a-b)^2013=[1/2-(-1/2)]^2013
=1^2013
=1