Function of this year!
Algebra
Level
5
Let \(f:\mathbb{N}^+ \to \mathbb{Q}^+\) satisfies \(f(1) = 2016\) and \(\displaystyle \sum_{i=1}^n f(i) = n^2 f(n)\) for \(n>1\).
If the value of \(f(2016)\) can be represented as \(\dfrac {a}{b}\) where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b\)?
by
Sharky Kesa