### Why do this
problem?

It
provides an easy starter where all students ought to have success.
It may seem surprising that some circles contain points with
rational coordinates and others do not. The second half can be
proved using modulus arithmetic and an argument by
contradiction.

### Key Question

What if the circle$x^2 + y^2 = 3$ DID contain rational
points...?

### Possible support

The article

Modulus Arithmetic and a Solution to Dirisibly Yours gives a
beginnersintroduction to modulus arithmetic and it is a good idea
to try the problem

Dirisibly Yours first.