MathDB

Let

r

and

s

be real numbers in the interval

[1, \infty)

such that for all positive integers

a

and

b

with

a \mid b \implies \left\lfloor ar \right\rfloor

divides

\left\lfloor bs \right\rfloor

.
a) Prove that

\frac{s}{r}

is a natural number.
b) Show that both

r

and

s

are natural numbers.
Here,

\lfloor x \rfloor

denotes the greatest integer that is less than or equal to

x

Problem Statement