RU-ALLRUSSIAN 1978 Problem 7

Let $\mathrm{p}(\mathrm{x}) = \mathrm{x}^{2} + \mathrm{x} + 1$ . Show that for every positive integer n, the numbers n, $\mathrm{p}(\mathrm{n})$ , $\mathrm{p}(\mathrm{p}(\mathrm{n}))$ , $\mathrm{p}(\mathrm{p}(\mathrm{p}(\mathrm{n})))$ , ... are relatively prime.