Question

Whether p\equiv q\pmod m when p = 83, q=-23, and m = 6.

Polynomial factorization
ANSWERED
asked 2021-03-19
Whether \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\) when p = 83, q=-23, and m = 6.

Expert Answers (1)

2021-03-21
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 \(\displaystyle{x}={y}\pm{o}{d}{m}\). This relation is called as congruence modulo m.
Calculation:
Given numbers are p = 83,q = —23, and m = 6.
For being congruence 83 + 23 = 106 has to be divisible by 6.
Note that, 106 = 17*6 +4.
Here, remainder is 4.
Therefore, 106 is not divisible by 6.
Therefore, when p = 83, q=-23, and m =6, \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\).
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