Is it obligatory for us to make up a day in Ramadan?

If the people of various towns agree on the moon sighting, and a Muslim fasts for twenty-nine or thirty days based on their sighting, then there is no make-up fast due for him. This is based on the Prophet's (peace be upon him) saying: "The fast is on the day you fast, the Eid al-Fitr is on the day you break your fast, and the Eid al-Adha is on the day you offer your sacrifices." This hadith (definition) is interpreted to mean that fasting and breaking the fast should be done with the Muslim community. However, if a Muslim fasts for less than twenty-nine days, then he must make up the remaining days to complete the month to twenty-nine days.