Most Helpful Guy
How sure are you that everything he claims was false to simply make you jealous. Saying that he's cheated on you on many occasions with random girls is way too far-fetched and even insane to lie about. If you truly love him, you will have to let him go and give him sufficient amount of time to realize that you and I are meant for one another. Time is a big factor in fixing broken relationships and you have to give one another enough time to clearly see and reflect upon your relationship. I know this may seems redundant, but I hope that helps.
Most Helpful Girl
Wow, that's tough.
In all honesty, it sounds like breaking up might have been the best option. It sounds like you two have a bunch of growing to do on your parts until you could even be in another relationship. If he is telling the truth about not cheating, (I'm sorry, but that all sounds a little strange. Guys don't usually lie and say they are cheating. They lie to try and cover up that they are cheating) then he still has some real
Maturity issues to deal with. Because that's not okay, actually cheating or not, to put someone through that kind of emotial stress is not fair.
Long distance relationships are hard in general, I'm not sure whether your trying to get back together or remain friends. If it's the first, I'd really search within yourself to see if that's what you really want. If it's the second, then if give him and you some time.
Good luck (: