What is the ruling on a traveler praying behind a resident, while shortening the prayer? And what should someone who has done this for many years, and does not know the number of prayers, do?

The questioner must make up the prayers he shortened behind a resident imam, repeating them in full without shortening. He must estimate the number of missed prayers and continue praying until he is reasonably certain he has made up what is due. The evidence for this is that if a traveler prays behind a resident, he is obligated to complete the prayer, based on the Prophet's (peace be upon him) saying: "Indeed, the imam is appointed to be followed...," and also based on what was reported from Ibn 'Umar and Ibn 'Abbas. The prayer must be repeated in full, even if the traveler caught only a part of it or believed the imam was a traveler, because it was incumbent upon him in full from the outset.