# Maximum Divisor

Prove that the maximum power of 2 divisor of 3^{2n} – 1 is 2^{n+2}

- 5 August, 2012 -
- Article, Math Problems -
- Tags : 104 problems, number theory, titu
- 1 Comment

We’re basically asked to show that

The proof of this will be done through construction, although we will assume that in order to complete our proof.

First, we observe that , therefore we can rewrite as the product of two similar terms.

(1)

Hence, according to , it must be the case that , and therefore the maximum power of that divides is .

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