He was fasting then he traveled to another country where they started fasting later; should he fast thirty-one days?

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Check below answers in case you are looking for other related questions:
Differences in moon sighting between countries and its effect on those who travel from one to another
Why are the Muslims not united in their fasting?

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Related Answers:
They fasted then they went back to their homeland where Ramadaan had not yet begun
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Differences in moon sighting between countries and its effect on those who travel from one to another
Why are the Muslims not united in their fasting?

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