Which of the following groups have lived on the continent of South America for the longest time?

The answer is Native American. However, if we are talking about Native Americans in South America there were various tribes who were now living there. You have the Mayas and the Aztecs living in Mexico and the Incas of Peru. These people had their own civilization and had to farm as well as to build large structures which gave them a high level of intelligence. Further proof that of intelligence was they had their own calendar and knew mathematics as well as astronomy.