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A Left-truncatable prime is a prime which in a given base (say 10) does not contain 0 and which remains prime when the leading (left) digit is successively removed. For example, 317 is left-truncatable prime since 317, 17 and 7 are all prime. Taking the cue from this initial research, we attempt to find the possible solutions for the Pell’s equation for all choices of In this paper, we focused primarily on Pell’s equations involving the left-truncatable primes and present to you another mysterious series and pattern typically associated with the Pell’s equation. As we proceed through the research, we will bring to the fore the recurrence relations among the identified solutions.
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