from what I've heard, it all started with a fight between two brothers over a bowl of soup...
(Old Testament | Genesis25:30 - 34)
30 And Esau said to Jacob, Feed me, I pray thee, with that same red pottage; for I am faint: therefore was his name called Edom.
31 And Jacob said, Sell me this day thy birthright.
32 And Esau said, Behold, I am at the point to die: and what profit shall this birthright do to me?
33 And Jacob said, Swear to me this day; and he sware unto him: and he sold his birthright unto Jacob.
34 Then Jacob gave Esau bread and pottage of lentiles; and he did eat and drink, and rose up, and went his way: thus Esau despised his birthright.
The Muslims are came from Esau, and the Jews came from Jacob.... correct me if I am wrong, but I think the Koran starts out the same as the Bible - up until this point. In the Koran, Esau does not despise his birthright, does not sell his soul for pottage.