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A function f defined on the positive integers (and taking positive integers values) is given by:
\begin{matrix} f(1) = 1, f(3) = 3 \\ f(2n) = f(n) \\ f(4n + 1) = 2f(2n + 1) - f(n) \\ f(4n + 3) = 3f(2n + 1) - 2f(n)\text{,} \end{matrix}
for all positive integers n. Determine with proof the number of positive integers \leq 1988 for which f(n) = n.

Slični zadaci

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