Functional Equations

Algebra Level 5

\[ \large f(km)+f(kn)-f(k)f(mn)\geq 1 \]

Denote a function \(f:\mathbb{N}\rightarrow \mathbb{R}\) such that it satisfy the equation above for all \(k,m,n\).

Find the sum of squares of all possible values of \(f(2015)\) .

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