A BDMO functional equation problem.

Choosing $y=-x$, we have that $2f(x^2) = f(f(0))$, in other words $f$ is constant on square numbers. From the initial condition we can deduce a bunch of things, one of them is that $f(1010^2) = 505$. So $505$ is the value on all squares, including $f(2025) = f(45^2)$.

The Cantor distribution is singular (with respect to lebesgue measure)

Every map $G$ from $Y^* \to X^*$ can be expresed as $T^*$ where $T: X \to Y$ [duplicate]

Are the conditions for completeness over a valued field equivalent?

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Space form structure for non orientable surfaces

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Two players drawing balls from an urn until the first red ball is selected

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Does the derivative of a differentiable function attain its maximum and minimum?