What is an easy, efficient way to do these sort of problems?

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- Jun 22nd 2010, 05:31 PMdwsmithFind a and b where a, b \in\mathbb{Z}^+

What is an easy, efficient way to do these sort of problems? - Jun 22nd 2010, 06:05 PMchiph588@
- Jun 22nd 2010, 06:07 PMdwsmith
What do you mean by just choose an exponent?

- Jun 22nd 2010, 06:08 PMchiph588@
- Jun 22nd 2010, 06:11 PMdwsmith
- Jun 22nd 2010, 06:13 PMchiph588@
- Jun 22nd 2010, 06:14 PMdwsmith
Then there are 5*4=20 possibilities to try.

- Jun 22nd 2010, 06:19 PMchiph588@
- Jun 22nd 2010, 06:28 PMundefined
- Jun 22nd 2010, 06:30 PMdwsmith
- Jun 22nd 2010, 06:32 PMchiph588@
- Jun 22nd 2010, 06:35 PMdwsmith
Is there a way to do permutations of the exponents to solve all the solutions or must I just plug them in?

- Jun 22nd 2010, 06:38 PMchiph588@
- Jun 23rd 2010, 12:35 AMmelese
Here is another solution.

Since , you can write and , where and are relatively prime.

Beacuse , and then .

Now choose such that . There are 8 possible ways. - Jun 23rd 2010, 05:59 AMdwsmith