..已知:a+1/a=1,求a^2004+1/a^2004

{一}a+1/a=1
(a+1/a)^2=1
a^2+1/a^2+2=1
{二}a^2+1/a^2=-1
(a^2+1/a^2)（a+1/a）=a^3+1/a^3+1/a+a=-1
{三}a^3+1/a^3=-2
(a^3+1/a^3)(a+1/a)=-2
{四}a^4+1/a^4=-2+1=-1
(a^4+1/a^4)(a+1/a)=-1
{五}a^5+1/a^5=-1+2=1
.（4个一循环）
所以a^2004+1/a^2004=-1