Roots with common tails

2015/08/29 by Alexandra Hobby, Hobby, Alexandra, David Hobby +1
Mathematics · #11A55 (Primary) #12F10 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A55 #msc:12F10

paper · pdf · doi:10.48550/arxiv.1508.07490

13 pages, no figures

arxiv created 2015/08/29 · arxiv updated 2015/09/01

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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