A Generalised Balancing Sequence and Solutions of Diophantine Equations \(x^2\pm pxy + y^2\pm x = 0\)
DOI:
https://doi.org/10.26713/cma.v13i1.1698Keywords:
Diophantine equation, Balancing sequencesAbstract
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, \(x^{2} \pm pxy + y^{2} \pm x =0\) and express its solutions in terms of generalised balancing sequences.
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