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x8-1

becomes

(x4 + 1) (x4 - 1) - perfect square

and then

(x4 + 1) (x2 - 1)(x2 + 1) - perfect square again.

and then

(x4 + 1)(x2 + 1)(x + 1)(x - 1) - perfect square again

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13y ago

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