# Math Help - [SOLVED] Coprime

1. ## [SOLVED] Coprime

Hi, i'm having trouble with the following questions;

Let a, b be non-zero integers.

a) Show that if there are x,y in Z (integers) with ax + by =1, then a and b are coprime.

b) Show that the integers a/(a,b) and b/(a,b) are coprime.

Thanks for you help.

2. 1) Let d such as $d|a$ and $d|b$

Then $d|ax+by\Rightarrow d|1\Rightarrow d=1$
So, a and b are coprime.

2) Let $d=(a,b)$

Then $a=da_1, \ b=db_1$ with $(a_1,b_1)=1$

But $\frac{a}{d}=a_1, \ \frac{b}{d}=b_1$, so $\frac{a}{d}, \ \frac{b}{d}$ are coprime.