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Let \(\mathbb{R}\) be the set of real numbers. Let \(f : \mathbb{R} \to \mathbb{R}\) be a function such that for all real numbers \(x\) and \(y,\)

\(f(x^2) + f(y^2) = [f(x + y)]^2 - 2xy\)

Let

\(S = \sum_{n = -2019}^{2019} f(n)\)

Determine the number of possible values of \(S.\)

 Dec 23, 2021
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There are 2019 different possible values of S.

 Dec 24, 2021

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