Do i need a router to connect to xbox live?

My xbox 360 is in my bedroom upstairs while my computer is downstairs. I have a modem that i'm not using but its a dsl modem (one port) but the modem im using with my computer has multiple ports (im sharing the modem with my dad's computer as well). Well i tried to connect to xbox live with my dsl modem without a router or computer. Everything connected perfectly until it connects to xbox live. I got an error saying there wasn't a sufficent amount of MTU or something. I searched the internet for a bit for anyone with a similar problem and someone said you need a router. But another guy said you needed a wireless modem or something. This is really confusing. If I can't use my dsl modem, do i have to use the modem my computer uses?