Solutions of the Pell equations x2-(a2+2a)y2=N via generalized Fibonacci and Lucas numbers
Abstract
In this study, we find continued fraction expansion of sqrt(d) when d=a2+2a where a is positive integer. We consider the integer solutions of the Pell equation x2-(a2+2a)y2=N when N=-1,+1,-4,+4. We formulate the n-th solution (xn,yn) by using the continued fraction expansion. We also formulate the n-th solution (xn,yn) via the generalized Fibonacci and Lucas sequences.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.