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Problem statement: Solution: Let’s note that Placing Since in . Replacing is not a solution. That means that such that in the original equation, we get: is constant and generates all values, we get that in the original equation: Changing the values of and we get that: Because the right sides are equal, the left sides must be equal, hence: Replacing Since : generates all values in , we get that: Placing x=0 in the original equation, we get: Cancelling terms, we get that Replacing . . in the original equation we get: generates all values … Substituting the last equation in : Replacing From we have: Substituting in the original equation we see that this solution satisfies the conditions given. Special thanks to AOPS member obi1kenobi for helping solve this problem.