Abu Ayyub al-Ansari told that God’s messenger said, “If anyone fasts during Ramadan, then follows it with six days in Shawwal, it will be like a perpetual fast.”
Mu'adha al-‘Adawiya said she asked ‘A'isha whether God’s messenger used to fast three days every month, and she replied that he did. She asked which days in the month he fasted, and she replied that he did not care which days of the month he fasted.
He said that when God’s messenger was asked about fasting on Monday he said, “On it I was born and on it the revelation was first sent down to me.”*
*The meaning seems to be that as this day is so distinguished, one could not choose a better one.