NASA's Next Mars Lander to Begin Construction

I've also wondered if you could use beamed microwave power to power a Mars airplane. For example, you could have a solar base station on the surface, and every hour or so the airplane would circle it closely and recharge its batteries. This only makes sense if you can make the microwave rectenna on the airplane much lighter than the equivalent solar cells. An airplane that never needs to land has some definite advantages. On the other hand, an easy way of acquiring geological samples is not one of them.

Another alternative is that you can use CO2 as an oxidizer -- Magnesium, for example, will burn in a C02 environment. Building a jet engine that runs on Magnesium is probably a non-trivial exercise, though!

If you really want to build a Mars airplane, I think nuclear is clearly the way to go. I don't know how you would test it though, since we tend to frown on running unshielded nuclear reactors these days.