Question

The value of the operation [9]+[8] in Z_{13} and to write the answer in the form [r] with 0\leq r < m.

Congruence
ANSWERED
asked 2021-03-22

The value of the operation \([9]+[8] \in\) \(\displaystyle{Z}_{{{13}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).

Expert Answers (1)

2021-03-24

Definition used:
Congruence.
Let m be an integer greater than 1. If x and y are integers, then x is congruent to y modulo m if \(x - y\) is divisible by m. It can be represented as \(\displaystyle{x}={y}\pm{o}{d}{m}\). This relation is called as congruence modulo m.
Calculation:
It is known that, \([x] + [y] = [x+y]\).
Then, the value of the expression becomes as follows.
\([9] + [8] = [9 + 8]=[17]\)
Since \(\displaystyle{17}\equiv{4}\pm{o}{d}{13}\). Thus \([9] + [8] = [4] \in\) \(\displaystyle{Z}_{{{13}}}\).
Therefore, the value of the expression is [4].

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