Abu Zharr al-Ghafari reported: “The Messenger of Allah ordered us to fast for three days of every month – that is, on the days of the full moon (the 13th, 14th, and 15th of the lunar month). And he said: ‘It is like fasting the whole year.'” This is related by an-Nasa’i and by Ibn Hibban, who called it sahih.
It is related that the Prophet would fast on Saturday, Sunday, and Monday of one month and on Tuesday, Wednesday, and Thursday of the next month. He would also fast for three days at the beginning of the month, or on the first Thursday and the next two Mondays of the month.