Roots with common tails
Alexandra Hobby, David Hobby

TL;DR
This paper characterizes cubic polynomials with three real roots sharing the same continued fraction tail and explores similar phenomena in lower-degree polynomials.
Contribution
It provides a complete characterization of cubic polynomials with roots having common continued fraction tails and extends the analysis to lower-degree cases.
Findings
Identifies conditions for roots to share a common continued fraction tail
Characterizes all such cubic polynomials over the integers
Examines similar properties in polynomials of degree less than three
Abstract
Some cubic polynomials over the integers have three distinct real roots with continued fractions that all have the same common tail. We characterize the polynomials for which this happens, and then investigate the situation for other polynomials of low degree.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Analytic Number Theory Research
