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== Degeneracy ==
{{ping|GaseousButter}} I corrected your edit as I think you meant "if k = 1" not "if n = 1", but let me know if I got the result wrong! [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 23:41, 1 July 2024 (UTC)
:Thank you - I was transcribing directly from the book but then changed the letters to match with the article - that n slipped through the cracks it seems! [[User:GaseousButter|GaseousButter]] ([[User talk:GaseousButter|talk]]) 13:37, 4 July 2024 (UTC)
== Skolem problem ==
"For example, the Skolem problem is decidable for sequences of order up to 4"
It would do to be more precise here - what is currently published in the literature is that the Skolem problem is decidable for algebraic sequences of order up to 3, and '''real''' algebraic sequences up to order 4. In fact, it is true that it is decidable for all algebraic sequences up to order 4 - I have a paper in the works about that so watch this space ;). But as of now what is written is a little ambiguous and potentially misleading. [[User:GaseousButter|GaseousButter]] ([[User talk:GaseousButter|talk]]) 13:48, 4 July 2024 (UTC)
:Thanks, I can fix this! From the source (Ouaknine and Worrell) I have: "Partial progress towards decidability of the Skolem Problem has been achieved by restricting the order of linear recurrence sequences. For sequences of order 1 and 2, decidability is relatively straightforward and considered to be folklore. Decidability for orders 3 and 4, however, had to wait until the 1980s before being independently settled positively by Mignotte, Shorey, and Tijdeman [13], as well as Vereshchagin"
:so I guess they are referring to real algebraic sequences? I can also check the original sources and add these. Or feel free to propose an edit. Thanks! [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 19:05, 6 July 2024 (UTC)
::Yes, in that source you cited the way they define a linear recurrence sequence is to be over the reals. I think the best thing to do is to cite the original sources (they're not the nicest things to read through being from the 80s). I might edit it myself in a bit but I was originally being lazy because I didn't want to figure out what the cleanest wording would be haha [[User:GaseousButter|GaseousButter]] ([[User talk:GaseousButter|talk]]) 19:02, 16 July 2024 (UTC)
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