Hi Avok, A simple answer is that the "un" indicate an indefinite noun. salamun= peace; as-salam= the peace. There's no big difference in the meaning in both cases. And salamun alaykum is mentioned in the Qur'an several times, as well as as-salam. So they're both correct.
The greeting "as-salaam 'alaykum" literally means "peace be upon you," and is a traditional greeting among Muslims. Because the majority of Arabs are Muslims, it is also the most common Arabic greeting. The response to this greeting is "wa 'alaykum as-salaam," which essentially means "and also with you."
salaam. Arabic or Muslim greeting, 1610s, from Arabic salam (also in Urdu, Persian), literally "peace" (compare Hebrew shalom ); in full, (as)salam 'alaikum "peace be upon you," from base of salima "he was safe" (compare Islam, Muslim ). Formerly used generically of ceremonious salutations in India and elsewhere in Asia.
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what does salaam alaikum salam mean