MathDB

Let

p, q

and

r

be positive real numbers such that the equation

\lfloor pn \rfloor + \lfloor qn \rfloor + \lfloor rn \rfloor = n

is satisfied for infinitely many positive integers

n{}

. (a) Prove that

p, q

and

r

are rational. (b) Determine the number of positive integers

c

such that there exist positive integers

a

and

b

, for which the equation

\left \lfloor \frac{n}{a} \right \rfloor+\left \lfloor \frac{n}{b} \right \rfloor+\left \lfloor \frac{cn}{202} \right \rfloor=n

is satisfied for infinitely many positive integers

n{}

Problem Statement