Document Type : Primary Research paper
PG and Research Department of Mathematics, Bishop Heber College (Autonomous, affiliated Bharathidasan University), Trichy, Tamil Nadu, India.
Department of Mathematics, Ayya Nadar Janaki Ammal College (Autonomous, affiliated to Madurai Kamaraj University), Sivakasi, Tamil Nadu, India.
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 type 𝜼𝟐=𝑫𝜻𝟐±𝜶, where the value 𝜶 is fixed positive integers. In this article, we look for non-trivial integer solutions to two negative Pell equations 𝒙𝟐=𝟐𝟔𝒚𝟐−𝟗𝒕,and 𝒙𝟐=𝟓𝟎𝒚𝟐−𝟑𝟒𝒕, 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.