What is the correct legal position we are obligated to take regarding the Ramadan fast, given that some of us fasted with the people of Mecca and others with the people of Oman, knowing that we are residents in India for study?

The Prophet, peace and blessings be upon him, commanded fasting Ramadan upon seeing the crescent moon. The crescent moon is confirmed by the sighting of a single upright witness, not by calculation. If the crescent moon is not sighted, then Sha'ban must be completed as thirty days. If people complete Sha'ban and then the crescent moon appears large, that holds no significance. Scholars differed on whether fasting becomes obligatory for all lands if the crescent moon is sighted in one land. The preponderant opinion is that each land has its own sighting. Therefore, if the questioners fasted on the day people in India fasted, their fast is valid.