Školjka

%V0 $$f(z) + f(\omega z + a) = g(z)$$ $$f(z) = g(z) - f(\omega z + a)$$ $$f(\omega z + a) = g(\omega z + a) - f(\omega^2 z + \omega a + a)$$ $$f(\omega^2 z + \omega a + a) = g(\omega^2 z + \omega a + a) - f(\omega^3 z + \omega^2 a + \omega a + a)$$ Sada imamo $\omega^3 = 1$, $\omega \neq 1$ i $1 + \omega + \omega^2 = \dfrac{1 - \omega^3}{1 - \omega} = 0$, pa je $$f(\omega^2 z + \omega a + a) = g(\omega^2 z + \omega a + a) - f(z)$$ Uvrštavamo u početnu jednadžbu: $$f(z) + \!\left( g(\omega z + a) - \left( g(\omega^2 z + \omega a + a) - f(z) \right) \right) = g(z)$$ $$f(z) = \frac12 \left( g(z) - g(\omega z + a) + g(\omega^2 z + \omega a + a) \right)