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Solve Equation with Floor Function Sum

Source: Canadian Mathematical Olympiad - 1981 - Problem 1.

May 27, 2011
functionfloor functionalgebra proposedalgebra

Problem Statement

For any real number tt, denote by [t][t] the greatest integer which is less than or equal to tt. For example: [8]=8[8] = 8, [π]=3[\pi] = 3, and [−5/2]=−3[-5/2] = -3. Show that the equation [x]+[2x]+[4x]+[8x]+[16x]+[32x]=12345[x] + [2x] + [4x] + [8x] + [16x] + [32x] = 12345 has no real solution.
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