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An equation involving the floor function

Source: Bundeswettbewerb Mathematik 2018, Round 1 - #2

June 30, 2018
algebraequationreal numbersfloor functionfunction

Problem Statement

Find all real numbers xx satisfying the equation ⌊20x+18⌋+⌊x+1820⌋=1.\left\lfloor \frac{20}{x+18}\right\rfloor+\left\lfloor \frac{x+18}{20}\right\rfloor=1.
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