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Equation involving floors

Source: South African MO 2004 Q3

May 27, 2012
floor functionceiling functionfunctionalgebranumber theory unsolvednumber theory

Problem Statement

Find all real numbers xx such that x⌊x⌊x⌊x⌋⌋⌋=88x\lfloor x\lfloor x\lfloor x\rfloor\rfloor\rfloor=88. The notation ⌊x⌋\lfloor x\rfloor means the greatest integer less than or equal to xx.
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