Power multiples in binary recurrence sequences: an approach by congruences
Teresa Boggio, Andrea Mori
TL;DR
This paper presents a simple congruence-based method to identify q-th power multiples in binary recurrence sequences, effectively proving their non-existence in many cases.
Contribution
It introduces an elementary approach using congruences to analyze power multiples in binary recurrence sequences, expanding the tools available for such problems.
Findings
No q-th power multiples found in many binary recurrence sequences
The method simplifies the proof process for non-existence of power multiples
Applicable to a broad class of binary recurrence sequences
Abstract
We introduce an elementary congruence-based procedure to look for q-th power multiples in arbitrary binary recurrence sequences (q>2). The procedure allows to prove that no such multiples exist in many instances.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Coding theory and cryptography