THE ROLE OF CONTINUED FRACTIONS IN SOLVING PELL-TYPE EQUATIONS VIA (γ,δ)-JACOBSTHAL AND(γ,δ)-JACOBSTHAL-LUCAS SEQUENCES

In this manuscript, the techniques for finding the solutions in terms of (γ,δ)- Jacobsthal and (γ,δ)- Jacobsthal Lucas sequences for two distinct categories of the Diophantine equations u_n^2-(p^2±q) v_n^2=q^2n and u_n^2-(4p^2 q^2-8 ) v_n^2=(-2δ)^n, n≥1, δ∈Z-{0} where p and q are specialised prime numbers, including Gaussian prime, Good prime, Lucky prime, Chen prime and Circular prime are offered. Moreover, the entire solutions discovered are confirmed with the assistance of three distinct Python codes. KEYWORDS: (γ,δ)- Jacobsthal, (γ,δ)- Jacobsthal Lucas, Gaussian prime, Good prime, Lucky prime, Chen prime, Circular prime.