I found on the Internet (here if you speak French) without any proof nor reference the following result.
Let $G$ be a non abelian simple group. Then $G$ is generated by a pair of elements.
In other words, there exists $(g_1,g_2)\in G^2$ such that $G=\langle g_1,g_2\rangle$.
How someone would prove such a result? Do you have any references where this is done? Is it a known fact (I have found nothing on the Internet)?