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floor(x/m)=floor(x/(m-1)), # of solutions

Source: Croatia 2000 1st Grade P3

May 8, 2021
algebrafloor function

Problem Statement

Let m>1m>1 be an integer. Determine the number of positive integer solutions of the equation ⌊xm⌋=⌊xm−1⌋\left\lfloor\frac xm\right\rfloor=\left\lfloor\frac x{m-1}\right\rfloor.
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