Answer in 2 steps?

Algebra Level 5

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

A function f:SSf:\mathbb{S} \rightarrow \mathbb{S} is defined as -f(x2+y2)=y2f(x)+x2f(y)+x4+y4f(x^2+y^2) = y^2f(x)+x^2f(y) +x^4+y^4

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


Give it a thought -

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

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