Periodic Patterns and Block Structures in Squared Pell Sequence Modulo 10e

Rima Patel and Devbhadra Shah
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Rima Patel: Department of Humanities and Social Science, Mahavir Swami College of Polytechnic, Bhagwan Mahavir University, Surat, India
Devbhadra Shah: Department of Mathematics, Veer Narmad South Gujarat University, Surat, India

International Journal of Research and Scientific Innovation, 2025, vol. 12, issue 5, 1165-1175

Abstract: In this paper, we investigate the periodic properties of the squared Pell sequence {}, which is defined by the recurrence relation for all ; with , where denotes th Pell number. For any modulus , we introduce a novel concept of ‘blocks’ within this sequence by examining the distribution of residues over a single period of the squared Pell sequence. Our results reveal that the length of any given period of the squared Pell sequence comprises either 1 or 2 blocks.

Date: 2025
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