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The Pell equations x^2-(k^2-1)y^2 = k^2, k ∈ N, k ≥ 2 Imprimitive and primitive solution classes
2020
Applied Mathematical Sciences
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Our subject is the family of Pell equations 2 − ( 2 − 1) 2 = 2 with parameter ∈ ℕ, ≥ 2. Each equation is trivially solvable by ( , 0), and each solution set can be separated by an appropriate equivalence relation into finitely many solution classes. The elements of the trivial solution class, containing ( , 0), are represented by Chebshev polynomials. Depending on , properties of primitive solution classes, whose elements ( , ) have coprime components, and imprimitive solution classes are
doi:10.12988/ams.2020.912173
fatcat:a73vzv5wfzae5lysebn6cvsp6a