List of number groups. The groups are cyclic with a generator number and a prime number for Modul. This is very important for Cryptography.

## Excercise statement-1

Group-1

The Group-1 is: generator=1, module=5, operation=Addition The final of the Group-1 it is when we search 0, because 0 its a neutral element of the Addition.

Group-2

The group 2 is: generator=2, module=17, operation=Addition The final of the Group-2 it is when we search 0, because 0 its a neutral element of the Addition.

Group-3

The group 3 is: generator=5, module=83, operation=Addition The final of the Group-3 it is when we search 0, because 0 its a neutral element of the Addition.

## Excercise statement-2

Group-4

The Group-4 is: generator=2, module=17, operation=Multiplication The final of the Group-3 it is when we search 1, because 1 its a neutral element of the Multiplication.

Group-5

The Group-5 is: generator=2, module=87, operation=Multiplication The final of the Group-3 it is when we search 1, because 1 its a neutral element of the Multiplication.

Group-6

The Group-6 is: generator=5, module=523, operation=Multiplication The final of the Group-3 it is when we search 1, because 1 its a neutral element of the Multiplication.

## Other Exercise

In this Exercise

the operation with parameter is: Addition or Multiplication; Generator=X, Module=Y. There is a parameter to be chosen by the user.

Parameterized number groups. Choose the operation, the generator and the prime number

Other Question.

### Result-3 Operation=For parameter

Observations

1. All the numbers of module are prime (5,17,83, 87, 523 etc.) Why?
2. All the groups are cyclic and not repeat a number. Attention whit this.
3. Others