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Now here we going to discuss with a new type of addition which is known as “addition modulo m” and written in the form  where  and  belongs to an integer and  is any fixed positive integer.
By definition we have
Where  is the least non-negative remainder when , i.e., the ordinary addition of and , is divided by .
For example,  , since  , i.e., is the least non-negative reminder when  is divisible by .
Thus to find , we add  and  in the ordinary way and then from the sum, we remove integral multiples of in such a way that the reminder is either or a positive integer less than .
When and  are two integer such that is divisible by a fixed positive integer , then we have . Which is read as “a is concurrent to b mod m”.
Thus, if and only if is divisible by . For example  since  is divisible by ,  ,  ,  .
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