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Forum: Number Theory Discussion Group 2020-10-01, 22:15
Replies: 22
Views: 12,102
Posted By jshort
Let S_{1} = 4 = (2 + \sqrt{3}) + (2 - \sqrt{3})...

Let S_{1} = 4 = (2 + \sqrt{3}) + (2 - \sqrt{3}) and S_{n+1} = S_{n}^{2} - 2.

We'll first prove via induction that S_{n} = (2 + \sqrt{3})^{2^{n-1}} + (2 - \sqrt{3})^{2^{n-1}}.

Clearly S_{1} =...
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