Question 35
Given positive integers $a, b, c$ with the property $b \gt 2a$ and $c \gt 2b$.
Show that there is then always a real number $r$ with the following property:
The fractional parts of the numbers $ra, rb, rc$ are all in the interval $\left( \frac{1}{3}, \frac{2}{3} \right)$.
(Note: The fractional part of a number is the difference between the number and its whole part.)
Show that there is then always a real number $r$ with the following property:
The fractional parts of the numbers $ra, rb, rc$ are all in the interval $\left( \frac{1}{3}, \frac{2}{3} \right)$.
(Note: The fractional part of a number is the difference between the number and its whole part.)