Can anyone prove the following?
given n numbers [integer and not necessary distinct] and lets denote the sum of all those number by Sum(n) then we have one of the following facts:
1- Sum(n) is Divisible By n.
2- if Sum(n) is not Divisible By n then [Sum(n) - x] is Surely Divisible By n where x is one of those given numbers.
example: given 1 , 2 , 3 there sum is 6 then 6 is divisible by 3
another example 1 , 2 , 3 , 4 there sum is 10 not divisible by 4 but if we take 10 - 2 yield 8 that's divisible by 4
anyone can help me to prove this?