# 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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