In Theorems in the form of "if and only if" such that the proof of one direction is extremely EASY to prove and the other one is extremely HARD, bof suggested the question in the title is more interesting, which motivates me to create this list. So my request is:
Theorems in the form of "if and only if" that the proofs of BOTH directions are nontrivial. The 'if and only if' formulation should be as natural as possible.
Thanks in advance.