# 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 $$a+b$$?

×