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Equation with Floor Functions

Source: Pan African MO 2012 Day 1 Q3

October 14, 2012
functionfloor functionalgebra proposedalgebra

Problem Statement

Find all real solutions xx to the equation ⌊x2−2x⌋+2⌊x⌋=⌊x⌋2\lfloor x^2 - 2x \rfloor + 2\lfloor x \rfloor = \lfloor x \rfloor^2.
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