# Prove that every ne N can be written as a product of an odd integer and a power of 2.

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• Jul 13th 2010, 07:50 AM
jess0517
Prove that every ne N can be written as a product of an odd integer and a power of 2.
Hey, Forum i was wondering if anyone would be kind enough to help me.
In order to start this problem, would i first have to make an equation following the example given? How would i then use n for even and for odd in the equation?

Prove that every ne N can be written as a product of an odd integer and a power of 2.
• Jul 13th 2010, 07:54 AM
chiph588@
If $n=2k$ and we assume inductively that $k=2^a\cdot(2b+1)$, then $n=\ldots$