I'm reading a lot about the Erdős-Straus Conjecture (ESC), a conjecture that states that for every natural number $p \geq 2$, there exists a set of natural numbers $a, b, c$ , such that the following equation is satisfied:
In my textbook the conjecture is proved for the following cases:
$$p=3\mod4 \\ p=2\mod3$$
But I know ESC has also been proven for: $$p=2\mod5\\ p=3\mod5\\ p=3\mod7\\ p=5\mod7\\ p=6\mod7\\ p=5\mod8$$
I also know these proofs are more difficult, but I'm just curious where I can find a summary of them all.