# The 100 followers problem!

Algebra Level 5

Given that

$\frac{ x}{y} + \frac{ y}{z} + \frac{ z}{x} = 0,$

the value of

$\frac{x^{14}z^7+y^{14}x^7+z^{14}y^7}{(x^{10}z^5+y^{10}x^5+z^{10}y^5)(x^{4}z^2+y^{4}x^2+z^{4}y^2)}$

can be expressed as $$\frac a b$$ for coprime positive integers. What is $$a+ b$$?

×