- Title
- Periods Of Ducci sequences and odd solutions to a Pellian equation
- Creator
- Breuer, Florian
- Relation
- Bulletin of the Australian Mathematical Society Vol. 100, Issue 2, p. 201-205
- Publisher Link
- http://dx.doi.org/10.1017/S0004972719000212
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2019
- Description
- A Ducci sequence is a sequence of integer n -tuples generated by iterating the map D:(a1,a2,…,an)↦(|a1−a2|,|a2−a3|,…,|an−a1|). Such a sequence is eventually periodic and we denote by P(n) the maximal period of such sequences for given n . We prove a new upper bound in the case where n is a power of a prime p≡5(mod8) for which 2 is a primitive root and the Pellian equation x2−py2=−4 has no solutions in odd integers x and y.
- Subject
- Ducci sequence; Pellian equation; cyclotomic field; real quadratic unit
- Identifier
- http://hdl.handle.net/1959.13/1463514
- Identifier
- uon:46758
- Identifier
- ISSN:0004-9727
- Language
- eng
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