Reverse it!

Number Theory Level pending

For positive integers n,

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)

How many possible values of n (which is less than or equal to 1988) are there so that f(n)=n?

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