Prove that any semisimple Lie algebra can be generated with two elements

Question

I saw this question on a previous test paper of Lie algebra. I tried using Cartan decomposition yet got no clue what to do next.

Answer 1

Over an arbitrary field we have the following result:

Theorem: Let $L$ be a finite-dimensional simple Lie algebra in characteristic $p\neq 2,3$. Then $L$ is generated by $2$ elements.

Proof: See here, Theorem A.

For a proof for semisimple Lie algebras in characteristic zero see Kuranishi's proof here, §2, Theorem $6$.