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f(n) = f(f(n + 11)) if n<=1999, f(n) = n - 5 if n > 1999

Source: Nordic Mathematical Contest 1999 #1

October 3, 2017
functional equationalgebra

Problem Statement

The function ff is defined for non-negative integers and satisfies the condition f(n)=f(f(n+11))f(n) = f(f(n + 11)), if n≤1999n \le 1999 and f(n)=n−5f(n) = n - 5, if n>1999n > 1999. Find all solutions of the equation f(n)=1999f(n) = 1999.
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