Solutions of Negative Pells Equation Invoving Pierpont Primes, Consecutive Good and Proth Primes

Many researchers have been devoted to nding the solutions (; ) in the set of non-negative integers, of Diophantine equation (Pell Equation) of the type 2 = D2 , where the value is xed positive integers. In
this article, we look for non-trivial integer solutions to the negative Pell equation x2 n= y2 t , where ; are the Pierpont Primes, Consecutive Good and Proth Primes, here t 2 N, for the dierent choices of t particular by
(i) t = 1, (ii) t = 3,(iii) t = 5,(iv) t = 2k, (v) t = 2k + 5,for all k 2 N.

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The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.