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Show that every Pythagorean triple (x, y, z) with x, y, z having no common factor...

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Advance Math

Show that every Pythagorean triple (x, y, z) with x, y, z havingno common factor d > 1 is of the form (r^2 - s^2, 2rs, r^2 +s^2) for positive integers r > s having no common factor > 1;that is

x = r^2 - s^2, y = 2rs, z = r^2 + s^2.

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