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Find the total number of different integers of a function

Source: IMO LongList 1988, Hong Kong 1, Problem 25 of ILL

October 22, 2005
functionalgebra unsolvedalgebra

Problem Statement

Find the total number of different integers the function f(x)=[x]+[2⋅x]+[5⋅x3]+[3⋅x]+[4⋅x] f(x) = \left[x \right] + \left[2 \cdot x \right] + \left[\frac{5 \cdot x}{3} \right] + \left[3 \cdot x \right] + \left[4 \cdot x \right] takes for 0≤x≤100.0 \leq x \leq 100.
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