Progress on the Skolem Problem

The Skolem Problem is the question of determining whether a given linear recurrence sequence (such as the Fibonacci numbers) contains a zero or not. Its decidability has been open for almost a century. The last major breakthroughs, dating back from the early 1980s and employing advanced machinery from analytic number theory and Diophantine approximation, concern linear recurrence sequences of small order (4 or less). Very recently, new techniques (some relying on certain central conjectures in number theory) have enabled substantial further advances on the Skolem Problem. We present a survey of recent developments in the field. This talk is based on joint work with Yuri Bilu, Richard Lipton, Florian Luca, Joël Ouaknine, David Purser, and James Worrell.

Authors

• Joris Nieuwveld

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