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[[User:Hoarwithy|Hoarwithy]] ([[User talk:Hoarwithy|talk]]) 13:35, 8 September 2011 (UTC)
:::: '''[9, 12, 15] is easily produced using Dickson's equations, as the example in VI ''clearly'' shows ( ''r'' = 6, ''s'' = 3, ''t'' = 6). You keep saying that you can find no proof that "Dickson’s equations produce non-primitive triples". This single example should be proof enough! Your other example, triple [15, 20, 25] is also easily produced using (''r'' = 10, ''s'' = 5, ''t'' = 10). Nowhere in the source you cite does Dickson limit himself to the primitives or non-primitives as you have repeatedly and inaccurately claimed. This is because (as he well knew) his equations apply to both cases! To get as many non-primitives using Dickson's equations as we want, we need only require that factor pairs ( ''s'' and ''t'' ) share a common factor, and begin with ''r'' = 2. A source for Dickson's proof? For starters you can look at his own footnote (34) on page 169 of the book you have cited. See also P.G. Egidi, D. Gambioli, A. Bottari, and H. Shotten [''Footnotes 35, 36, 39, and 36a on the same page'']. '''
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