RADical cyclic function, dude!

Algebra Level 3

If a periodic non-zero function \(f(x)\) exists such that \(\sqrt{3}f(x) = f(x - 1) + f(x + 1),\) what is its fundamental period?

Note: A function \(g(x)\) is periodic if there exists some \(T\) such that \(g(x) = g(x + T)\) for all \(x.\) The fundamental period is the minimum positive \(T\) such that this property holds.

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