Question

# Whether p\equiv q\pmod m when p=21, q=53, and m=8.

Polynomial factorization
Whether $$\displaystyle{p}\equiv{q}\pm{o}{d}{m}$$ when p=21, q=53, and m=8.

2021-05-02
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, $$\displaystyle{p}\equiv{q}\pm{o}{d}{m}$$.