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Abstract
Many researchers have been devoted to finding the solutions (η,ζ) in the set of non-negative integers, of Diophantine equation (Pell Equation) of the typeη^2=Dζ^2±α, where the value α is fixed positive integers. In this article, we look for non-trivial integer solutions to two negative Pell equations x^2=13y^2-17^t, and x^2=113y^2-97^t, t∈N for the different choices of t particular by (i) t=1, (ii) t=3,(iii) t=5,(iv) t=2k,(v) t=2k+5,∀ k∈N. Additionally, recurrence relations on the solutions are obtained.
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