Large prime divisor conjecture for cyclotomic-type quotients

Let $z$ and $y$ be relatively prime positive integers with $z>y$, and let $n$ be an odd prime integer. Consider the integer

$$\frac{z^n-y^n}{z-y}.$$

Large prime divisor conjecture. There exists a prime divisor $p$ of this integer such that $p>z$. The paper presents this as an observation suggested by computations and proposes it as a possible route toward better understanding these integers and related Diophantine equations; no proof or resolution is given.