'Abdullah b. Amr (Allah be pleased with them) reported that the Messenger of Allah (ﷺ) had said to him:

Observe fast for a day and there would be reward for you for the rest (of the days). He said: I am capable of doing more than this. He then said: Observe fast for two days, and there would be reward for you for the rest (of the days). He said: I am capable of doing more than this. He (the Prophet) said: Observe fast for three days and there would be reward for you for the rest of the days. He said: I am capable of doing more than this, whereupon he said: Observe fast for four days and there would be reward for you for the rest of the days. He said: I am capable of doing more than this. Thereupon he said: Then observe fast (which is the) best in the eye of Allah, the fast of David (peace be upon him) ; he used to observe fast one day and break on the other day.

حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا غُنْدَرٌ، عَنْ شُعْبَةَ، ح وَحَدَّثَنَا مُحَمَّدُ بْنُ الْمُثَنَّى، حَدَّثَنَا مُحَمَّدُ بْنُ جَعْفَرٍ، حَدَّثَنَا شُعْبَةُ، عَنْ زِيَادِ بْنِ فَيَّاضٍ، قَالَ سَمِعْتُ أَبَا عِيَاضٍ، عَنْ عَبْدِ، اللَّهِ بْنِ عَمْرٍو - رضى الله عنهما - أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ لَهُ ‏"‏ صُمْ يَوْمًا وَلَكَ أَجْرُ مَا بَقِيَ ‏"‏ ‏.‏ قَالَ إِنِّي أُطِيقُ أَكْثَرَ مِنْ ذَلِكَ ‏.‏ قَالَ ‏"‏ صُمْ يَوْمَيْنِ وَلَكَ أَجْرُ مَا بَقِيَ ‏"‏ ‏.‏ قَالَ إِنِّي أُطِيقُ أَكْثَرَ مِنْ ذَلِكَ ‏.‏ قَالَ ‏"‏ صُمْ ثَلاَثَةَ أَيَّامٍ وَلَكَ أَجْرُ مَا بَقِيَ ‏"‏ ‏.‏ قَالَ إِنِّي أُطِيقُ أَكْثَرَ مِنْ ذَلِكَ ‏.‏ قَالَ ‏"‏ صُمْ أَرْبَعَةَ أَيَّامٍ وَلَكَ أَجْرُ مَا بَقِيَ ‏"‏ ‏.‏ قَالَ إِنِّي أُطِيقُ أَكْثَرَ مِنْ ذَلِكَ ‏.‏ قَالَ ‏"‏ صُمْ أَفْضَلَ الصِّيَامِ عِنْدَ اللَّهِ صَوْمَ دَاوُدَ - عَلَيْهِ السَّلاَمُ - كَانَ يَصُومُ يَوْمًا وَيُفْطِرُ يَوْمًا ‏"‏ ‏.‏