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

Abstract

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.