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Let f f f be a non-constant polynomial such that f(x−1)+f(x)+f(x+1)=f(x)22013x f(x-1) + f(x) + f(x+1) = \frac {f(x)^2}{2013x} f(x−1)+f(x)+f(x+1)=2013xf(x)2 for all nonzero real numbers x x x. Let N N N the sum of all possible values of f(1) f(1) f(1). Find the remainder when N N N is divided by 1000 1000 1000.
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