Question

What elements are generating in the group of addition of the remainders modulo 10?

Answer 1

Ответ:

{1, 3, 5, 7, 9}

Объяснение:

As known, generating element $p$ in finite cyclical group $|C_{n}|=n$   satisfy to the next condition

$gcd(p, n)=1$

Also, it is necessary and sufficient conditions for elements in $C_{n}$

Therefore, for $n=10$ we get p={1,3,5,7,9}

Answer 2

The group of addition of the remainders modulo 10 consists of the integers from 0 to 9, where the operation is addition followed by taking the remainder when divided by 10. This group is also known as the additive group modulo 10.

In this group, you have the following elements:

1. 0
2. 1
3. 2
4. 3
5. 4
6. 5
7. 6
8. 7
9. 8
10. 9

The operation of addition in this group follows the rules of modular arithmetic. For example, if you add 7 and 5, the result is 12, but when you take the remainder modulo 10, you get 2. Similarly, if you add 8 and 6, you get 14, and taking the remainder modulo 10 gives you 4.