Ghalib bin Farqad said: Sayyiduna Anas bin Malik (may Allah be pleased with him) used to give the salam to his right and to his left, saying: "As-salamu alaykum wa rahmatullah (Peace and the mercy of Allah be upon you)."
Hadith Referenceالمعجم الكبير للطبراني / باب الألف / 690