Im from abroad, can somebody please help me prove this GCD problem

Results 1 to 5 of 5

- Nov 8th 2016, 02:36 PM #1

- Joined
- Nov 2016
- From
- United States
- Posts
- 2

- Nov 8th 2016, 03:51 PM #2

- Joined
- Apr 2005
- Posts
- 18,954
- Thanks
- 2739

## Re: GCD problem

Your attachment says (a/(a, b), b/(a,b)). Since this is titled "GCD problem" I presume that (x, y) here means the greatest common divisor of a and b. Let x be the GCD of a and b. Then a= cx and b= dx for some integers c and d are integers that have

**no**factors in common (If c= pq and d= pr then a= pqx and b= prx so that the greatest common divisor is px, not x). So a/(a,b)= c and b/(a,b)= d and, since they have no common divisors, (a/(a,b), b/(a,b)) is 1.

- Nov 8th 2016, 04:21 PM #3

- Joined
- Feb 2015
- From
- Ottawa Ontario
- Posts
- 1,567
- Thanks
- 293

- Nov 8th 2016, 05:32 PM #4

- Nov 8th 2016, 07:08 PM #5

- Joined
- Nov 2016
- From
- United States
- Posts
- 2