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# Pythagorean Families

Let $$(a,b,c) = v, (a',b',c') = v'$$and $$a,a',b,b',c,c'$$ be non-negative integers such that $$f(x,y,z) = x^{2} + y^{2} - z^{2} = 0$$ whenever $$f$$ is evaluated at $$v$$ or $$v'$$ $$v$$ is said to lie in the same family as $$v'$$ if $$v = nv'$$ for $$n$$ a positive integer or one's reciprocal. The question i ask is how many distinct families of solutions of $$f(x,y,z) = 0$$ are there.

Note by Samuel Queen
3 years, 3 months ago