I was wondering if someone could help me prove the following.

Let (a, b)=1. let d|ab. show that their exists unique such that

Printable View

- Nov 23rd 2010, 06:58 PMChris11Relitivly prime, unique divisors of divisors
I was wondering if someone could help me prove the following.

Let (a, b)=1. let d|ab. show that their exists unique such that - Nov 23rd 2010, 08:07 PMDrexel28
- Nov 24th 2010, 07:24 AMPetek
@Drexel28 - In your example, we have a = 4, b = 17 and d = 4. If we let and , then it seems to me that we've met the requirements of the problem.

@Chris11 - Are you allowed to use the Fundamental Theorem of Arithmetic (i.e., unique factorization) in your solution? If so, that's a hint. - Nov 24th 2010, 08:40 AMOpalg
You could start by letting . Then divides , so let . Also, there exist integers , such that . Multiply that equation by , and use the fact that is a multiple of to conclude that divides .

For the uniqueness, you could try to show that must necessarily be equal to .