HF RL Explorer

Task 822

Task 822: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. 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 $x.$ Find the sum of all possible values of $f(1).$

The task

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 $x.$ Find the sum of all possible values of $f(1).$