By Dr. Muzammil Siddiqi
Fasting six days of the month of Shawwal is mentioned in a Prophetic hadith. Prophet Muhammad (peace and blessings be upon him) said, “Whosoever fasted in Ramadan and then followed up with six fasting days of Shawwal, it is like fasting every day.” (Muslim)
The meaning is that the reward is like the reward of a person who he had fasted a whole year. It is highly recommended to fast six days of the month of Shawwal, but it is not obligatory. Those who want to fast can fast after Eid Al-Fitr any six days during Shawwal.
It is not required to fast six days continuously without any interruption. One can fast according to convenience any time during the month.
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Source: www.aboutislam.net