Define a *Primitive Pythagorean Triple* as a set of three positive integers \((a,b,c)\) such that \(a<b<c\) and \(a^2 + b^2 = c^2\), and where the integers \(a,b,c\) don't all share a common factor greater than 1.

How many *Primitive Pythagorean Triples* exists that satisfy the equation \(a+b-c = 20\) ?

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