A Generalised Balancing Sequence and Solutions of Diophantine Equations \(x^2± pxy + y^2± x = 0\) - Kameswari, P. Anuradha; Anoosha, K. (Communications in Mathematics and Applications, 2022)
We consider a generalization of balancing sequences and investigate some properties of the generalised balancing sequences in this paper. For a positive integer \(p\) we solve for the Diophantine equations, \(x^{2} ± pxy + y^{2} ± x =0\) and express its solutions in terms of generalised balancing sequences.
Keywords: Diophantine equation; Balancing sequences