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, \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\).

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, \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\).