In algebra and number theory, what plain-spoken questions are deceivingly complicated?

Question

A while ago, I asked my professor how we could determine whether a particular curve intersected lattice points; that is, had a solution of integer pairs. They did not know, and I learned later I had effectively asked about the two-variable case of Hilbert's tenth problem.

I would like examples of questions like these which

1. Are plain-spoken, to some degree,
2. Are easily comprehensible,
3. Have unknown solutions, or solutions which require methods far beyond students who have reached the point they can ask the question sensibly to obtain.

Some of my own examples:

1. The above problem.
2. The Riemann hypothesis.
3. (debatably easily comprehensible) proof that the axioms of arithmetic are consistent.