Guess The Golden Function

Algebra Level 5

\[ \large h(h(n))+h(n+1)=n+2\]

Consider all functions \(h:\mathbb N \to \mathbb N\) satisfying the functional equation above for all natural numbers \(n\).

Find the value of \(h(2014)\).

Hint: Try to find some initial values and then somehow try to bring the Golden Ratio into use. Golden Ratio is \(\frac{1+\sqrt{5}}{2}\).


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