(x^7 + x) - (y^7 + y) = x(x^6 + 1) - y(y^6 + 1)= x(x^3 + 1)(x^3 - 1) - y(y^3 + 1)(y^3 - 1)= x(x+1)(x^2-x+1)(x-1)(x^2+x+1) - y(y+1)(y^2-y+1)(y-1)(y^2+y+1)
(x^7 + x) - (y^7 + y) = x(x^6 + 1) - y(y^6 + 1)
= x(x^3 + 1)(x^3 - 1) - y(y^3 + 1)(y^3 - 1)
= x(x+1)(x^2-x+1)(x-1)(x^2+x+1) - y(y+1)(y^2-y+1)(y-1)(y^2+y+1)