Let \(\mathbb{S}\) be the set \(\mathbb{R}^+ \cup \{0\}\)

A function \(f:\mathbb{S} \rightarrow \mathbb{S} \) is defined as -\[f(x^2+y^2) = y^2f(x)+x^2f(y) +x^4+y^4\]

Then the value of \(f(2015)\) can be written as \(a^d b^d c^d\) where \(a,b,c,d\) are all distinct prime numbers. Find the value of \(a+b+c+d\).

**Give it a thought** -

\(\bullet\) Will the answer change if \(\mathbb{S}\) was replaced by \(\mathbb{R}\) (Real numbers) or \(\mathbb{C}\) (Complex numbers)?

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