Hi (Hi)

Prove that if , where and are positive integers, and is a positive odd integer, then

Result due to Gauss or Euler... I can't remember... more likely to Gauss

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- Jun 21st 2009, 01:22 AMMooDivisibility
Hi (Hi)

Prove that if , where and are positive integers, and is a positive odd integer, then

Result due to Gauss or Euler... I can't remember... more likely to Gauss - Jun 21st 2009, 01:33 AMsimplependulum
Isn't it ?

If it is correct , then ... since

Therefore ,

Finally , sub. x into 2

- Jun 21st 2009, 01:42 AMTheAbstractionist
The fact that is odd means that the expression will end in Hence

- Jun 21st 2009, 01:47 AMsimplependulum
Is it true for all positive integers

??

Therefore ,

If , then . - Jun 21st 2009, 02:03 AMTheAbstractionist
- Jun 21st 2009, 02:14 AMMoo