Mathegoras

Functions › Functional equations › Extremes in functional equations

Distinct values of a symmetric function

High school · ●●●●○ 100 pts

Given a function ff for which f(x)=f(398−x)=f(2158−x)=f(3214−x)f(x) = f(398 - x) = f(2158 - x) = f(3214 - x) for all real xx, what is the largest number of different values that can appear in the list f(0),f(1),f(2),…,f(999)f(0), f(1), f(2), \ldots, f(999)?

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periodic functionssymmetry of functions