Show that can't be a power of 2 if ( ).

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- Nov 18th 2009, 12:32 PMjames_bondNot a power of 2
Show that can't be a power of 2 if ( ).

- Nov 18th 2009, 04:29 PMtonio
- Nov 19th 2009, 07:57 PMNonCommAlg
the claim would be true if we also assume that n > 1. the proof is quite easy: let it's clear that if is even, then is odd.

so we may assume that is odd. the proof now is by__induction__over we have suppose is a power of 2. then for

some and so which is never a power of 2 because if then the identity completes the proof. - Nov 19th 2009, 07:59 PMDrexel28
- Nov 20th 2009, 12:22 AMNonCommAlg
- Nov 20th 2009, 12:24 AMDrexel28
- Nov 24th 2009, 12:11 PMjames_bond