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 that p = 21,q = 53, and m = 8.

For being congruence 21 — 53 = 32 should be divisible by 8.

Note that, -32 = -4*8 +0

Here, the remainder is 0.

Therefore —32 is divisible by 8.

Therefore, When p =21, q=53, and m = 8, \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\).

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 that p = 21,q = 53, and m = 8.

For being congruence 21 — 53 = 32 should be divisible by 8.

Note that, -32 = -4*8 +0

Here, the remainder is 0.

Therefore —32 is divisible by 8.

Therefore, When p =21, q=53, and m = 8, \(\displaystyle{p}\equiv{q}\pm{o}{d}{m}\).