Plethora of Pythagorean triples

True or False: Every odd number greater than 1 is the smallest member of a primitive Pythagorean triple.

Note: A primitive Pythagorean triple is a triple of positive integers \((a,b,c)\) such that \(a^2+b^2 = c^2\) and \(\gcd(a,b,c) = 1.\)

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