Solutions of equations x2−(p2q2±3p)y2=±kt

Abstract

In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences. With the help of this equation, we have found units of Z[885]and Z[915]in terms of generalized Fibonacci, generalized Lucas, generalized Pell and generalized Pell–Lucas numbers.

Keywords

• Generalized Fibonacci numbers
• Generalized Lucas numbers
• Generalized Pell numbers
• Generalized Pell–Lucas numbers