Show that every positive integer n has a unique expression of the form n=2rm,r greater or equal 0, m a postive odd integer

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- Sep 6th 2009, 02:19 AMblazingmathUnique expression of an integer
Show that every positive integer n has a unique expression of the form n=2rm,r greater or equal 0, m a postive odd integer

- Sep 6th 2009, 02:58 AMDavidEriksson
From the

*"Unique*-*Prime*-Factorization Theorem" we can write . Now let r be a number such that but and let . Then , where and m is odd from the construction of r. This is a unique expression from the "*Unique*-*Prime*-Factorization Theorem".