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

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

"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.

The bisectors of two angles of a triangle are of equal length if and only if the two bisected angles are equal. If the two angles are equal, the triangle is isosceles and the proof is very easy. However proving that a triangle must be isosceles if the bisectors of two of its angles are of equal length seems to be quite difficult.