I see that their prices are much lower than some other 3rd party websites
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LOL, what I think you mean is, the prices they *say* they sell flights *from* are printed as lower than some other third party websites print their false prices..
In fact for most of them, even when you press "purchase" they just tell you to wait up to a day and they will confirm, and then they will say "hey guess what that price is gone but for only another $200 (which BTW now is more expensive than the airline) we can sell you that flight? Don't want to take it, OK give us a few months and we'll get around to refunding your money"
... .. think I'm kidding? Unfortunately not :-(
If you believe any of the prices advertised on these sort of websites, can I recommend a nice guy that will sell you some swampland in Florida, sorry I mean prime waterfront real estate.
Just buy from the airline far too many scammers out there.