Springfield Armory, Rock Island Arsenal, and Remington all made M1903's. They have the barrel mounted rear sight. Those rifles were originally equipped with the S-style stock. Put any of those rifles in a C-stock, and it is "technically" a M1903A1.

Remington's M1903 production phased into the M1903A3, which it produced, along with Smith Corona. Difference being the rear sight configuration and the milled steel parts changed to stamped steel.

For reference - M1903 Springfield - Wikipedia, the free encyclopedia

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