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I am seeking for a way to find modulo of a sequence of numbers like: (a1 + a2 + a3 + a4 + ... + an) mod x
Is there any way/property of modulo function so that I can compute mod of this sequence from the individual mods of numbers in sequence.
391
Case 1: When N < K, for each number i, N >= i >= 1, will give i as result when operate with modulo K. So, the required sum will be the sum of the first N natural number, N*(N+1)/2.
Now here we are going to discuss a new type of addition, which is known as “addition modulo m” and written in the form a+mb, where a and b belong to an integer and m is any fixed positive integer. By definition we have. a+mb=r,for0⩽r<m.
Mathematically, the modulo congruence formula is written as: a ≡ b (mod n) , and n is called the modulus of a congruence. where r is a common remainder.
10 modulus 2 stands for the Euclidean division discussed, defined and explained in full detail on our home page. 10 is the dividend, 2 is the divisor (modulo), 5 is the quotient explained below, and 0 is called the remainder. The division rest of 10 by 2 equals 0, and the value of the quotient is 5.
Mod operator is distributive;
( x + y ) % z
... is equivalent to:
( x % z + y % z ) % z
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