Generalised Ap\'ery numbers modulo $9$
C. Krattenthaler (Universit\"at Wien), Thomas W. M\"uller (Queen, Mary, University of London)
TL;DR
This paper characterizes the behavior of generalized Apéry numbers modulo 9, confirming two conjectures related to their modular properties and advancing understanding of recursive sequences in modular arithmetic.
Contribution
It provides a complete characterization of generalized Apéry numbers modulo 9 and proves two conjectures from prior work on mod-3^k behavior of recursive sequences.
Findings
Established the modular behavior of generalized Apéry numbers modulo 9
Proved two conjectures from previous research on mod-3^k sequences
Enhanced understanding of recursive sequences in modular arithmetic
Abstract
We characterise the modular behaviour of (generalised) Ap\'ery number modulo , thereby in particular establishing two conjectures in "A method for determining the mod- behaviour of recursive sequences" [arXiv:1308.2856].
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Coding theory and cryptography