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Looks like a Remington Model 10. Call Remington with a serial number, they could tell you a little more. You can post more of the serial number here, too, someone my know.
Post a few more number. Leave the last 2 or three digits as an "X"
It could also be a model 29 (built from 1929 to 1933), the improved model 10. My model 29 is my favorite shotgun. It's a little heavy by todays standards but I shoot it better than any of my other shotguns.
The U prefix was use for the Model 10. This model was made from 1908 to 1929 and ended with serial number 275,600. The Model 29 ended with serial number 38,000. With the U prefix and serial number, your shotgun has to be a model 10.
Loren RSA