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:: Euclid and Dickson have proved that their equations produce ALL Pythagorean triples. The proofs are easy enough to follow and you can find them with little effort if you really want to understand them. However, it appears you have some other agenda. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/184.153.109.223|184.153.109.223]] ([[User talk:184.153.109.223|talk]]) 06:09, 5 September 2011 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
If you are referring to Euclid’s equation in the write-up in Entries I and II, “Pythagorean Triple”, this merely suggests non-primitives can be obtained by separately multiplying a b c, in primitives <math>a^2 + b^2 = c^2</math>, by a multiplier k. This was referred to in my original XIII entry as the only way non-primitives could be produced from the standard equation results, is also not appropriate to this equation because m and n produce some non-primitives, is not mentioned by Dickson or the other Professors, and is not referenced to Euclid.
I have not found any proof that Dickson’s equations produce non-primitive triples.
You say Dickson and Euclid proved that their equations produce ALL triples, and these are easily understood and found with little effort. I would be obliged if you could quote references to where this is claimed, and show me the values of m and n that produce the triples 9. 12. 15, and 15. 20. 25. This information would settle this dispute. If you can’t then I would ask you to reinstate that section of my work extending Dickson’s work, which you deleted.
Shall we say two weeks from now (September 22) would be an adequate time scale for this?
[[User:Hoarwithy|Hoarwithy]] ([[User talk:Hoarwithy|talk]]) 13:35, 8 September 2011 (UTC)hoarwithy
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