MathDB

a) Prove that every sub-group

(A,+)

of group

(\mathbb{Z},+)

is in the form

A=n \cdot \mathbb{Z}

for some

n \in \mathbb{Z}

where

n \cdot \mathbb{Z}=\{n \cdot x/x\in\mathbb{Z}\}

.
b) Using problem (a) , prove that the greatest common divisor

d

of non zero integers

a_1, a_2,... ,a_n

is given by relation

d=\lambda_1a_1+\lambda_2 a_2+...\lambda_n a_n

with

\lambda_i\in\mathbb{Z}, \,\, i=1,2,...,n

Problem Statement