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:

Given numbers are p = 29,q = 34, and m =7.

For being congruence 29 - (-34) = 63 has to divisible by 7.

That is, 63 = 9*7+0.

Here, the remainder is 0. Therefore, 63 is divisible by 7.

Therefore, When p = 29,q = -34, and m = 7, \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\).

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:

Given numbers are p = 29,q = 34, and m =7.

For being congruence 29 - (-34) = 63 has to divisible by 7.

That is, 63 = 9*7+0.

Here, the remainder is 0. Therefore, 63 is divisible by 7.

Therefore, When p = 29,q = -34, and m = 7, \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\).