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FE, floor of polynomial

Source: Serbia MO 2005 3&4th Grades P3

April 11, 2021
functional equationfealgebrapolynomial

Problem Statement

Determine all polynomials pp with real coefficients for which p(0)=0p(0)=0 and f(f(n))+n=4f(n)for all n∈N,f(f(n))+n=4f(n)\qquad\text{for all }n\in\mathbb N,where f(n)=⌊p(n)⌋f(n)=\lfloor p(n)\rfloor.
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