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 [closed]

I believe this is a common phenomenon in mathematics, but surprisingly, no such list has been created on this site. I don't know if it's of value, just out of curiosity, I want to see more examples. So my request is:

Theorems in the form of "if and only if" that the proof of one direction is extremely EASY, or intuitive, or make use of some standard techniques (e.g. diagram chasing), while the other one is extremely HARD, or counterintuitive, or require a certain amount of creativity. The 'if and only if' formulation should be as natural as possible.

Thanks in advance.

Edit: I know this question is somewhat ill-posed. A better one: Theorems in the form of “if and only if” such that the proofs of BOTH directions are nontrivial

Solution 1:

Let $n$ be a positive integer. The equation $x^n+y^n=z^n$ is solvable in positive integers $x,y,z$ iff $n\le2$.

Solution 2:

"A compact 3-manifold is simply-connected if and only if it is homeomorphic to the 3-sphere."

One direction [only if] is the Poincaré conjecture. The other direction shouldn't be too bad hopefully.