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 \(\frac{1+\sqrt{5}}{2}\).
by
Souryajit Roy