If k > 2, and n = 2^{k-3}, show that 3^{n}is not congruent to 1 (mod 2^{k}).

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- Dec 7th 2012, 07:09 PMalexer1278help with proof for number theory, possibly using induction?
If k > 2, and n = 2

^{k-3}, show that 3^{n}is not congruent to 1 (mod 2^{k}). - Jan 1st 2013, 07:59 AMLordoftheFliesRe: help with proof for number theory, possibly using induction?
Old thread but if you're still interested: there are several ways to do this.

**1)**By induction for assume

etc.

**2)**A rather nice way is to consider

therefore the highest power of 2 dividing is 2

It follows that is the highest power of 2 dividing , so cannot divide