International Research Journal of Education and Technology

In this study, the solutions of the Diophantine Equation ,              where  and  are twin primes, cousin primes, safe primes in terms of generalised Pell and generalised Lucas sequences by employing continued fractions are studied. Correspondingly, all the derived solutions to these categories of equations are confirmed by Python programs.

Keywords: Generalised Pell and Pell Lucas sequence, twin primes, cousin primes, safe primes, continued fractions.