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

Printable View

- Nov 18th 2009, 11:32 AMjames_bondNot a power of 2
Show that can't be a power of 2 if ( ).

- Nov 18th 2009, 03:29 PMtonio
- Nov 19th 2009, 06:57 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, 06:59 PMDrexel28
- Nov 19th 2009, 11:22 PMNonCommAlg
- Nov 19th 2009, 11:24 PMDrexel28
- Nov 24th 2009, 11:11 AMjames_bond