Did Jesus Think Adam Was a Historical Figure?

The question here would be whether Jesus might simply be referring to the literary Adam, that figure that features in the stories of Genesis 2 and 3, rather than speaking of a historical individual. I think that's certainly very possible. We can refer to literary figures without committing ourselves to their historicity. Having said that, however, it does seem to me very plausible that Jesus of Nazareth believed that Adam (the Adam in the literary story) did exist. Therefore, even if his teaching doesn't imply the existence of a historical Adam, I think the fact that Jesus believed that Adam was a historical person would entail that Adam is historical because as a divine being Jesus must be omniscient and therefore cannot hold any false beliefs. Therefore, if he believed that Adam was a historical person, that entails that that belief was true and that therefore Adam was a historical person. So at one level I don't think that the teachings of Jesus entail that Adam was a historical figure, but if Jesus did believe that Adam actually lived and wrought then I think that does commit someone who believes in the deity of Christ to the historicity of Adam.