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Let X be a real linear topological space. We characterize solutions f:X → ℝ and M:ℝ → ℝ of the equation f(x+M(f(x))y) = f(x)f(y) under the assumption that f and M have the Darboux property.

J. Brzdęk [1] characterized Baire measurable solutions $f:X\to K$ of the functional equation $$f(x+f{\left(x\right)}^{n}y)=f\left(x\right)f\left(y\right)$$ under the assumption that $X$ is a Fréchet space over the field $K$ of real or complex numbers and $n$ is a positive integer. We prove that his result holds even if $X$ is a linear topological space over $K$; i.e. completeness and metrizability are not necessary.