2023 OIM Problems/Problem 6
Problem
Let be a polynomial of degree greater than or equal to 4 with integer coefficients. An integer is called -representable if there exist integers and such that . Prove that, if for all , more than half of the integers in the set are -representable, then all even integers are -representable or all odd integers are -representable.
Solution
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See also
https://sites.google.com/associacaodaobm.org/oim-brasil-2023/pruebas