HMMT 2002 U47

Guts
Answer

The real function $f$ has the property that, whenever $a, b, n$ are positive integers such that $a+b=2^{n}$ , the equation $f(a)+f(b)=n^{2}$ holds. What is $f(2002)$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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