MathDB

5

Part of 2020 Turkey MO (2nd round)

Problems(1)

Polynomial with real coefficients

Source: Turkey National Mathematical Olympiad 2020 P5

3/8/2021
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.
algebrapolynomialseriesalgebra proposedfloor function