Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $x$.)

share|cite|improve this question

1 Answer 1

up vote 1 down vote accepted

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 $x\le0$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.