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Old 2021-05-08, 16:50   #7
Charles Kusniec
Charles Kusniec's Avatar
Aug 2020

616 Posts

Dear a1call,

Thanks for the example.

I like you used 65 as an example, because this is one of those cases of multiplicity of primitive Pythagorean triangle.

At 65, we have 2 solutions because we have 2 ways to make the Pythagorean triangle.

That’s why I don’t really like how WolframAlpha and many others present this kind of solution.

The way they present it looks like we have 4 sequences of solutions, when in fact, we only have 2 sequences.

They should present only the sequences a(n) = 65 n^2 +- 8 n - 16 and a(n) = 65 n^2 +- 18 n - 15. These two sequences are at offset Zero.

For more details about offset I have a study that explains well this phenomenon...
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