Challenge Level

Find a fraction $\frac{m}{n}$ ($m \neq n$) such that all of the fractions

$$\frac{m}{n},\ \frac{m+1}{n+1},\ \frac{m+2}{n+2},\ \frac{m+3}{n+3},\ \frac{m+4}{n+4},\ \frac{m+5}{n+5}$$

can be simplified by cancelling.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.