The value of the operation [13]^{6} in Z_{15} and to write the answer in the form [r] with 0\leq r < m.

ankarskogC

ankarskogC

Answered question

2021-04-09

The value of the operation [13]6 in Z15 and to write the answer in the form [r] with 0r<m.

Answer & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-04-11Added 98 answers

Definition used:
Congruence.
Let m be an integer greater than 1. If xand yare integers, then x is congruent to y modulo m if x — y is divisible by m. It can be represented as x=y(b mod m). This relation is called as congruence modulo m.
Calculation:
Consider the values and congruence classes modulo m,
[13]6 and m = 15.
It is evident that [x]=[y] if [x=y(b mod m)]. Since 13=2(b mod 15).
Then,
[13]=[-2]
[13]6=[2]6
=[(2)6]
=[64]
Since, by the principal or congruence 64=4(b mod 15). Therefore, [13]6=[4] in Z15.
Therefore, the value of the expression is [4].

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