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.