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

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.