if p is prime and (a,b)=p, then (a^2,b^2)=?

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- January 27th 2010, 02:50 PMDeepuabstract algebra #2
if p is prime and (a,b)=p, then (a^2,b^2)=?

- January 28th 2010, 01:20 AMSudharaka
Dear Deepu,

Take

Now since, and

Therefore, and

Then since the gcd of "a" and "b" is "p" ; ---------------A

Also since and and

Then since the gcd of and is "k" ; ----------------B

From A and B ; p=k

Therefore

Hope this helps. - January 28th 2010, 02:16 PMDeepu
Thank you very much.

- January 28th 2010, 03:25 PMDefunkt
- January 28th 2010, 09:19 PMchiph588@
Suppose and

where .

Set . Then .

Now and .

So .

Hence . - January 28th 2010, 10:52 PMSudharaka