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Polynomial with real coefficients

Source: Turkey National Mathematical Olympiad 2020 P5

March 8, 2021
algebrapolynomialseriesalgebra proposedfloor function

Problem Statement

Find all polynomials with real coefficients such that one can find an integer valued series a0,a1,…a_0, a_1, \dots satisfying ⌊P(x)⌋=a⌊x2⌋\lfloor P(x) \rfloor = a_{ \lfloor x^2 \rfloor} for all xx real numbers.
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