MathDB

floor(x/y)=floor(nx)/floor(ny) for all n in N (Ukraine 1998 Grade 9 P4)

Source:

June 4, 2021

number theoryalgebrafloor function

Problem Statement

Real numbers

x

and

y

not less than

1

have the property that

\left\lfloor\frac xy\right\rfloor=\frac{\lfloor nx\rfloor}{\lfloor ny\rfloor}\enspace\text{for any }n\in\mathbb N.

Prove that either

x=y

x

and

y

are integers, one dividing the other.