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Vieta jumping

I've not come across Vieta jumping before, but apparently it can be used to solve in proving this:

\(\displaystyle 2+2\sqrt{12n^2+1} \in \mathbb{N} \Leftrightarrow \sqrt{2+2\sqrt{12n^2+1}} \in \mathbb{N}, n \in \mathbb{N}.\)

How? Is there a general form of problem that Vieta jumping is useful for? I've read the wikipedia page, but I don't find its explanation useful.

Note by A L
4 years ago

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I dont think this would require veita jumping from anywhere :3

Sagnik Saha - 3 years, 3 months ago

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