IMO Shortlist 1995 problem S3
Dodao/la:
arhiva2. travnja 2012. For an integer
let
be the least prime that does not divide
and define
to be the product of all primes less than
In particular,
For
having
define
Consider the sequence
defined by
and
for
Find all
such that
%V0
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