# The function for 2016

Algebra Level 5

For all positive integers $$x$$, a function $$f(x)$$ is defined as follows:

• $$f(1)=2016$$.
• $$f(1)+f(2)+f(3)+\cdots + f(n-1)+f(n)={ n }^{ 2 }f(n)$$ for $$x>1$$.

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

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