Solutions Of Negative Pell’s Equation Involving Interprimes

Document Type : Primary Research paper

Authors

1 PG and Research Department of Mathematics, Bishop Heber College (Autonomous, affiliated Bharathidasan University), Trichy, Tamil Nadu, India.

2 Department of Mathematics, Ayya Nadar Janaki Ammal College (Autonomous, affiliated to Madurai Kamaraj University), Sivakasi, Tamil Nadu, India.

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 type 𝜼𝟐=π‘«πœ»πŸ±πœΆ, where the value 𝜢 is fixed positive integers. In this article, we look for non-trivial integer solutions to two negative Pell equations π’™πŸ=πŸπŸ”π’šπŸ−πŸ—π’•,and π’™πŸ=πŸ“πŸŽπ’šπŸ−πŸ‘πŸ’π’•, 𝒕∈𝑡 for the different choices of 𝒕 particular by (π’Š) 𝒕=𝟏, (π’Šπ’Š) 𝒕=πŸ‘,(π’Šπ’Šπ’Š) 𝒕=πŸ“,(π’Šπ’—) 𝒕=πŸπ’Œ,(𝒗) 𝒕=πŸπ’Œ+πŸ“,∀ π’Œ∈𝑡. Additionally, recurrence relations on the solutions are obtained.

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