MathDB
x^3= f( [ x ] ) + g(x)

Source: 1998 Belarus TST 1.1

December 25, 2020
functionalfunctional equationalgebraperiodic

Problem Statement

Do there exist functions f:R→Rf : R \to R and g:R→Rg : R \to R, gg being periodic, such that x3=f(⌊x⌋)+g(x)x^3= f(\lfloor x \rfloor ) + g(x) for all real xx ?
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