Algebra · Floor function · Fractional part · Counting solutions
How many solutions does the equation
\[ x - 2019\{x\} = 2019 \]
have in the set of real numbers?
Here, for a real number \(x\), the symbol \(\lfloor x \rfloor\) denotes the greatest integer not exceeding \(x\), and \(\{x\}\) denotes the value \(x - \lfloor x \rfloor\).
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Serbian Regional Competition (Okruzno takmicenje) 2019, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source