Question

Q: The result of a mod b for integers a and b must be​

Answer 1

Answer:

For integers a and b, the outcome of a mod b must be congruent.

Step-by-step explanation:

The residue after dividing a by b is called a mod b.

The following is another technique to connect congruence and remainders. $3.4$ Theorem When a and b are divided by n, they provide the same remainder if a ≡ b mod. In contrast, if dividing a and b by n results in the same remainder, then a ≡ b mod n.

a ≡ b (mod n)

According to this, an is congruent to b mod n. means that when an is divided by n, b is the result.

It can be expressed mathematically as,

$a = kn+b, b < n$, k ∈N

For example, $5$≡$-9$ (mod 7).

There are exactly seven distinct congruence classes for modulo $7$; specifically, an integer is either congruent modulo $7$ to $0, 1, 2, 3, 4, 5,$ or $6$.

Or, to put it another way, the $7$ congruence classes are: {$0,-7,7,-14,14,$…}, {$1,-6,8,-13,15,$…}, {$2,-5,9,-12,16,$…} up to {$6,-1,13,-8,20,-15,$…}

Each time, all the numbers in one congruence class are congruent to those in that class, but not to any other numbers.

Congruence modulo $2$ is an intriguing specific case where all even integers are congruent to one another and all odd numbers belong to the other congruence class. Therefore, a number's congruence class modulo $2$ determines its "parity," such as whether it is odd or even.

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