# Playing with Primitive Pythagorean Triples!

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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