IMO Shortlist 1995 problem S3

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Dodao/la: arhiva
2. travnja 2012.
For an integer x \geq 1, let p(x) be the least prime that does not divide x, and define q(x) to be the product of all primes less than p(x). In particular, p(1) = 2. For x having p(x) = 2, define q(x) = 1. Consider the sequence x_0, x_1, x_2, \ldots defined by x_0 = 1 and

x_{n+1} = \frac{x_n p(x_n)}{q(x_n)} for n \geq 0. Find all n such that x^n = 1995.
Izvor: Međunarodna matematička olimpijada, shortlist 1995