Home Competitions ILL 1984 Problem 27
The function f ( n ) f(n) f ( n ) n n n f ( 0 ) = 0 , f ( 1 ) = 1 f(0) = 0, f(1) = 1 f ( 0 ) = 0 , f ( 1 ) = 1 f ( n ) = f ( n − 1 2 m ( m − 1 ) ) − f ( 1 2 m ( m + 1 ) − n ) f(n) = f\left(n -\frac{1}{2}m(m - 1)\right)-f\left(\frac{1}{2}m(m+ 1)-n\right) f ( n ) = f ( n − 2 1 m ( m − 1 ) ) − f ( 2 1 m ( m + 1 ) − n ) 1 2 m ( m − 1 ) < n ≤ 1 2 m ( m + 1 ) , m ≥ 2 \frac{1}{2}m(m - 1) < n \le \frac{1}{2}m(m+ 1), m \ge 2 2 1 m ( m − 1 ) < n ≤ 2 1 m ( m + 1 ) , m ≥ 2 n n n f ( n ) = 5 f(n) = 5 f ( n ) = 5
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