Let denote the greatest integer less than or equal to

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let [x][x] denote the greatest integer less than or equal to xx. If the number of positive integral solutions of the equation [x[x2]]=[x1+12]\left[\dfrac{x}{[x^2]}\right]=\left[\dfrac{x}{1+\frac12}\right] is nn, find nn.

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