2020 USOJMO Problems/Problem 6
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.)