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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.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1900IMO Shortlist 1995 problem A22
1902IMO Shortlist 1995 problem A40
1913IMO Shortlist 1995 problem NC15
1916IMO Shortlist 1995 problem NC43
1921IMO Shortlist 1995 problem S10
1925IMO Shortlist 1995 problem S50