Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
Qurʾān Bukhārī Muslim Nasāʾī Abū Dāwūd Tirmidhī Ibn Mājah Mālik Aḥmad Dārimī Ḥākim Ibn Ḥibbān Ṭabarānī Nasāʾī's Kubrá Bayhaqī al-Luʾluʾ wa-al-Marjān Ibn Rajab's Fifty Riyāḍ al-Ṣāliḥīn Aḥmad's Zuhd Suyūṭī
suyuti:1-113b – Masrūq
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السيوطي:١-١١٣b –

"عَنْ مَسْرُوقٍ قَالَ: كَانَ أَبُو بَكْرٍ يُسَلِّمُ عَنْ يَمِينِهِ وَعَنْ يَسَارِهِ: السَّلَامُ عَلَيْكُمْ وَرَحْمَةُ الله، ثُمَّ يَنْتَفِلُ سَاعَةً كَأَنَّهُ عَلَى الرَّضْفِ".  

[عب] عبد الرازق وابن سعد، والطحاوي

See similar narrations below:

Collected by Ṭabarānī
tabarani:10174 – al-Ḥusayn b. Isḥāq al-Tustarī > Maʿmar b. Sahl al-Ahwāzī > ʿImrān b. Mūsá > Sufyān > Mughīrah > Abū al-Aḥwaṣ > ʿAbdullāh

[Machine] The Prophet ﷺ used to greet with "Peace be upon you and the mercy of Allah, Peace be upon you and the mercy of Allah" on his right side and on his left side.  

الطبراني:١٠١٧٤ – حَدَّثَنَا الْحُسَيْنُ بْنُ إِسْحَاقَ التُّسْتَرِيُّ ثنا مَعْمَرُ بْنُ سَهْلٍ الْأَهْوَازِيُّ ثنا عِمْرَانُ بْنُ مُوسَى عَنْ سُفْيَانَ عَنْ مُغِيرَةَ عَنْ أَبِي الْأَحْوَصِ عَنْ عَبْدِ اللهِ

عَنِ النَّبِيِّ ﷺ أَنَّهُ كَانَ يُسَلِّمُ عَنْ يَمِينِهِ وَعَنْ يَسَارِهِ «السَّلَامُ عَلَيْكُمْ وَرَحْمَةُ اللهِ السَّلَامُ عَلَيْكُمْ وَرَحْمَةُ اللهِ»