Currently Being ModeratedMar 21, 2013 4:22 AM (in response to KeithBryant)
Apple ID and iTunes account are two different things. You can use different AppleID's and should for things like iCloud backup and such. But unless you want to pay twice for apps, I suggest you use one iTunes account.
It seems you made purchases under two different iTunes accounts which is why you are being asked to authenticate for that account.
Take a look here on how to use multiple devices with a single iTunes account.