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prove that (3+2√2)^2n-1 + (3-2√2)^2n-1 - 2 is a perfect integral square

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prove that (3+2√2)^2n-1 + (3-2√2)^2n-1 - 2 is a perfect integral square for every positive integer n.

Aug 12, 2021

#1
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(3+2√2)^2n-1 + (3-2√2)^2n-1 - 2

$$(3+2\sqrt2)^2*n-1 + (3-2\sqrt2)^2*n-1 - 2\\ =n(3+2\sqrt2)^2 + n(3-2\sqrt2)^2-4\\$$

Is this what you intended to write or do you need brackets anywhere?

Aug 13, 2021