(* Diophantus20.v *)
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(* Diophantus' 20th problem *)
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Require Export Descent.
Require Export Pythagorean.
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(* Some auxiliary lemmas *)
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(* Diophantus' problem *)
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Lemma for_mba_pytha2: forall m n u v a b : Z,
u * u = m * m + n * n -> v * v = n * n - m * m -> u - v = 2 * (b * b) ->
u + v = 4 * (a * a) -> b * b * (b * b) + 2 * (a * a) * (2 * (a * a)) = n * n.