``I Wanna Be Your Man'' is a Lennon--McCartney-penned song recorded and released as a single by the Rolling Stones, and then recorded by the Beatles. The song was primarily written by Paul McCartney, and finished by Lennon and McCartney in the corner of a room while Mick Jagger and Keith Richards were talking.

Is it true that did the beatles write any songs for the rolling stones?
yes