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comment Does anyone recognize this function?
Please accept my apologies if I am incorrect, but did your logic just go: f(2) = f(1+1) = f(1)*f(1) = (+1)^1 * f(1) = k? But that logic isn't correct. Using this logic, g(0) = g(1 + -1) = g(1) * g(-1), but if g(x) = x^2 then we get a contradiction (g(0) would be 0, g(1) * g(-1) = 1)