Problem 1. Find all functions f : R → R satisfying the following conditions : a) f(x + y) − f(x) − f(y) ∈ {0, 1} for all x, y ∈ R b) bf(x)c = bxc for all real x. ( Korea Winter, 2018 ) Problem 2. Find all functions f : R → R satisfying the following conditions : f(x 3 ) + f(y 3 ) = (x + y)(f(x