Question

# Whether p\equiv q\pmod m when p = 91, q=37, and m =9.

Congruence
Whether $$\displaystyle{p}\equiv{q}\pm{o}{d}{m}$$ when p = 91, q=37, and m =9.

2021-05-09
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 = 91,q = 37, and m = 9.
For being congruence 91 — 37 = 54 has to be divisible by 9.
That is 54 = 6*9 +0.
Here, remainder is 0.
Therefore, 54 is divisible by 9.
Therefore, when p = 91, q = 37, and m = 9, $$\displaystyle{p}\equiv{q}\pm{o}{d}{m}$$.