2020 USOJMO Problems/Problem 6
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Problem
Let be an integer. Let be a nonconstant -variable polynomial with real coefficients. Assume that whenever are real numbers, at least two of which are equal, we have . Prove that cannot be written as the sum of fewer than monomials. (A monomial is a polynomial of the form , where is a nonzero real number and , , , are nonnegative integers.)
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