If we began our fast in the Kingdom of Saudi Arabia, then we travelled to our country in East Asia during the month of Ramadhan, where the Islamic Hijri month is a day behind , should we fast 31 days?
If you fasted in Saudi Arabia or another land, then you fasted the rest of the month in your own land or another place, then break your fast with them(in the last land) even if that is more than 30 days. This is due to the statement of the Prophet-Sallallahu alaihi wassallam- The fast is the day that you all fast and breaking the fast is the day when you all break the fast. However, if you did not complete 29 days you must complete that (number of fasting days).This is because the month is not less than 29 days.
1.At-Tirmithi no. 697
Shaykh `Abdul-`Azeez Bin Baz Fatawa Islamiyah Page no.234 Vol: 2