1997 IMO Problems/Problem 6


For each positive integer $n$, let $f(n)$ denote the number of ways of representing $n$ as a sum of powers of $2$ with nonnegative integer exponents. Representations which differ only in the ordering of their summands are considered to be the same. For instance, $f(4)=4$, because the number 4 can be represented in the following four ways:


Prove that, for any integer $n \ge 3$,



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1997 IMO (Problems) • Resources
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