SOLUTIONS OF NEGATIVE PELL EQUATION INVOLVING TWIN PRIME

Let d not equal 1 be a positive non-square integer and N be any fixed positive integer. Then the equation x(2) - dy(2) = +/- N is known as Pell's equation named after the famous mathematician John Pell. In this paper, we fix d and N to be twin prime 41 and 43 and search for non-trivial integer solution to the equation x(2) = 41y(2) - 43(t), t is an element of N for the different choices of t given by (i) t = 1, (ii) t = 3, (iii) t = 5, (iv) t = 2k, and (v) t = 2k + 5, for all k is an element of N. Further, recurrence relation on the solutions are obtained.