向高手求教,此题如何解!

x-y=1,
x^3-y^3=4,
(x-y)(x^2+xy+y^2)=4,(x-y)^2+3xy=4,xy=1.
x^2+y^2=(x-y)^2+2xy=1+2=3.
x^4+y^4=(x^2+y^2)^2-2x^2y^2=9-2=7.
x^6+y^6=(x^4+y^4)(x^2+y^2)-x^2y^2(x^2+y^2)=21-3=18.
x^7-y^7=(x^4+y^4)(x^3-y^3)+x^3y^3(x-y)=28+1=29.
x^13-y^13=(x^6+y^6)(x^7-y^7)-x^6y^6(x-y)=522-1=521.

正确答案是:1

主要是利用立方差和完全平方的知识.
由x^3-y^3=(x-y)*(x^2+xy+y^2)
又x-y=1
可得x^3-3xy-y^3
=(x-y)*(x^2+xy+y^2)-3xy
=x^2+xy+y^2-3xy
=x^2-2xy+y^2
=(x-y)^2
=1