# An algebra problem by Aira Thalca

Algebra Level 3

Consider the recurrence relation $$f(1) + f(2) + \cdots + f(n) = n^2 \times f(n)$$ for $$n=2, 3,\ldots$$ with $$f(1) = 2016$$.

If the value of $$f(2016)$$ can be expressed as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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