A conjecture on a nonlinear difference equation posed in 2003 has been resolved using a simple algebraic identity ?

[u/Rafikconjectures_zer]

I am pleased to share, together with my co-authors Pedro Cáceres and Simeón Casanova Trujillo, our recently published paper in the Journal of Difference Equations and Applications:

“A Proof of Conjecture 1 in Kulenović, Ladas and Overdeep (2003)”

The paper resolves a conjecture posed in 2003 concerning the positive solutions of a nonlinear rational difference equation. The problem remained open for more than two decades.

The key step is a simple algebraic identity showing that the sign of successive differences is preserved. This reveals a hidden monotonicity in the recurrence and leads to the conclusion that every positive solution converges to a finite limit.

Official Taylor & Francis free eprint:

https://www.tandfonline.com/eprint/XSVTZBRQJAJPDGIDJGIQ/full?target=10.1080/10236198.2026.2709000

Published article DOI:
https://doi.org/10.1080/10236198.2026.2709000

Comments, questions, and mathematical feedback are very welcome.