Challenge Level

The 2 squares and 2 cubes cannot be prime

Could the squares also be cubes?

$(2\times2\times2)\times(2\times2\times2) = (2\times2)\times(2\times2)\times(2\times2)$ is a square and a cube, so yes

So you need 2 primes and 2 square-cubes

This problem is taken from the UKMT Mathematical Challenges.

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