# The Functional Equation that Trolled the NIMO Participants

Algebra Level 4

Let $$f$$ be a non-constant polynomial such that $f(x-1) + f(x) + f(x+1) = \frac {f(x)^2}{2013x}$ for all nonzero real numbers $$x$$. Let $$N$$ the sum of all possible values of $$f(1)$$. Find the remainder when $$N$$ is divided by $$1000$$.

×

Problem Loading...

Note Loading...

Set Loading...