Hadith: If you fast three days of the month, then fast the thirteenth, fourteenth and fifteenth

عن أبي ذر رضي الله عنه قال: قال رسول الله صلى الله عليه وسلم : «إِذَا صُمْتَ مِنَ الشَّهْرِ ثَلاَثاً، فَصُمْ ثَلاَثَ عَشْرَةَ، وَأرْبَعَ عَشْرَةَ، وَخَمْسَ عَشْرَةَ». عن قتادة بن ملحان رضي الله عنه قال: كانَ رسولُ اللهِ صلى الله عليه وسلم يَأمُرُنَا بِصِيَامِ أيَّامِ البِيضِ: ثَلاثَ عَشْرَةَ، وَأرْبَعَ عَشْرَةَ، وَخَمْسَ عَشْرَةَ. عن ابن عباس رضي الله عنهما قال: كانَ رسولُ اللهِ صلى الله عليه وسلم لاَ يُفْطِرُ أيَّامَ البِيضِ في حَضَرٍ وَلاَ سَفَرٍ.
[حديث أبي ذر حسن. حديث قتادة صحيح. حديث ابن عباس حسن] - [حديث أبي ذر رواه الترمذي والنسائي وأحمد. حديث قتادة بن ملحان رواه أبو داود والنسائي وابن ماجه. حديث ابن عباس رواه النسائي]

Abu Dharr (may Allah be pleased with him) reported that the Messenger of Allah (may Allah’s peace and blessings be upon him) said: "If you fast three days of the month, then fast the thirteenth, fourteenth and fifteenth." Qatādah ibn Milhān (may Allah be pleased with him) reported that the Messenger of Allah (may Allah’s peace and blessings be upon him) used to order us to fast the White Days: the thirteenth, fourteenth and fifteenth (of every lunar month)." Ibn ‘Abbās (may Allah be pleased with him) reported that the Messenger of Allah (may Allah’s peace and blessings be upon him) never broke his fast on the White Days, whether he was a resident or a traveler.”
Good hadith - Narrated by Ibn Majah

Explanation

Abu Dharr reported that the Messenger of Allah (may Allah’s peace and blessings be upon him) said: “If you fast”, O Abu Dharr. His statement, “of the month”, means any month. “Three (days)”, means you intended it voluntarily, “then fast the thirteenth, fourteenth and fifteenth”, means fast the 13th of the month and the two following days. These days are called the White Days – days of the white nights – because of their illumination by the full moon, and fasting them every month is recommended. Ibn ‘Abbās reported: "The Messenger of Allah (may Allah’s peace and blessings be upon him) never broke his fast on the White Days”, meaning the days of white nights, which are the 13th, 14th, and 15th, because they are lit up with the full moon from their beginning until their end, so fasting them is appropriate in gratitude to Allah, Exalted. His statement, “whether he was a resident or traveler” means that he adhered to fasting them in both cases. So, fasting such days is a confirmed act of Sunnah. It is more likely that his fasting the White Days is due to their being in the middle of the month, and the middle of anything is the most balanced part of it.