Sahih Al Bukhari 1: Chapter 2, Hadith 38

(38) To observe Saum [(fasts) (according to Islamic teachings)] during the month of Ramadan (sincerely and faithfully) hoping for Allah's Rewards only, is a part of faith

حَدَّثَنَا مُحَمَّدُ بْنُ سَلَامٍ، ‏‏‏‏‏‏قَالَ:‏‏‏‏ أَخْبَرَنَا مُحَمَّدُ بْنُ فُضَيْلٍ، ‏‏‏‏‏‏قَالَ:‏‏‏‏ حَدَّثَنَا يَحْيَى بْنُ سَعِيدٍ، ‏‏‏‏‏‏عَنْ أَبِي سَلَمَةَ، ‏‏‏‏‏‏عَنْ أَبِي هُرَيْرَةَ، ‏‏‏‏‏‏قَالَ:‏‏‏‏ قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ:‏‏‏‏ "مَنْ صَامَ رَمَضَانَ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ".

SAHIH HADITH:

Narrated Abu Huraira: Allah's Apostle said, Whoever observes fasts during the month of Ramadan out of sincere faith, and hoping to attain Allah's rewards, then all his past sins will be forgiven.

REFERENCE:

Sahih Al Bukhari 1: Chapter 2, Hadith 38