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Question P.170: Suppose we start with a Pythagorean triple (a, b, c) of posi......

Suppose we start with a Pythagorean triple (a, b, c) of positive integers, that is, positive integers a, b, c such that a² + b² = c² and which can therefore be used as the side lengths of a right triangle. Show that it is not possible to have another Pythagorean triple (b, c, d) with the same integers b and c; that is, show that b² + c² can never be the square of an integer.

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