1988 IMO Problems/Problem 3

A function $f$ is defined on the positive integers by $f(1) = 1, f(3) = 3, f (2n) = f (n)$ , $f(4n+1) = 2f(2n+1)−f(n)$ (Error compiling LaTeX. Unknown error_msg), $f(4n+3) = 3f(2n+1)−2f(n)$ (Error compiling LaTeX. Unknown error_msg) , for all positive integers $n$ . Determine the number of positive integers $n$ , less than or equal to $1988$ , for which $f(n) = n$ .