Quora: IMO 1988 Question 3

Problem A3

A function f is defined on the positive integers by:

for all 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)

Determine the number of positive integers n less than or equal to 1988 for which f(n) = n.

What is the explanation of the solution of problem 3 from IMO 1988? by Alon Amit


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