# Is there a way to tell for what range $\lfloor\frac xy\rfloor = n$?

Given $x$, is there a way to tell for what range of $y$ $$\left\lfloor\frac xy\right\rfloor = n?$$

(Where $\lfloor x\rfloor$ is the integer part of $x$.)

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You must have $$n\le\frac{x}{y}<n+1.$$ If $x>0$ then $y$ must be also positive, and you get $$\frac{x}{n+1}<y\le\frac{x}{n}.$$ I leave to you the case $x\le0$.