On the Order of the Padovan Companion Matrix Modulo Prime Powers

Key Points

• The aim is to investigate the order of the Padovan companion matrix under specific modular conditions.
• Characterization of Padovan sequences
• Examination of finite fields
• Mathematical analysis of matrix order modulo prime powers
• Identified specific properties of Padovan matrices in finite fields
• Established relationships between matrix order and prime powers
• Demonstrated examples of matrix order behavior in different modular settings