Floors Times Four

★ 6/10functions number theory Modular Arithmetic Casework

Problem

For $x \in \mathbb{R}$ , let

f(x) = \lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 6x \rfloor + \lfloor 8x \rfloor.

How many positive integers not exceeding $2024$ can occur as a value of $f(x)$ ?

Answer

Solution

Difficulty	6/10
Topics	functions, number theory, Modular Arithmetic, Casework

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