Tirmidhi

Hadith Commentary: Benefits and Issues:
From this hadith, it is understood that the practice of the Prophet (sallallahu alayhi wa sallam) was not fixed and constant, but he would encourage his companions to fast on the "white days" (Ayyam al-Beedh), i.e., the 13th, 14th, and 15th of the lunar month. Therefore, if one is to fast only three days, then these are the most virtuous days to do so.

Commentary:
Note:
(In the chain of narration, Khaythamah ibn Abi Khaythamah Abu Nasr Basri is weak in hadith transmission.)

Benefits and Issues:
From this, it is understood that apart from the middle days of the month, any three days can be observed as fasts, because the Prophet (sallallahu alayhi wa sallam) would sometimes fast three days without specifying or designating particular days, so that it would not be considered obligatory. In this way, sometimes he (sallallahu alayhi wa sallam) would fast three days at the beginning of the month; thus, those Companions (radi Allahu anhum) who were aware of these initial days narrated accordingly. Therefore, there is no contradiction between fasting on the white days (ayyam al-beedh) and fasting at the beginning of the month.

However, it is preferable to fast the three days of the white days (ayyam al-beedh), because the Prophet (sallallahu alayhi wa sallam) commanded this, as has been mentioned in hadith number 1707.