Abstract
In this paper, we study sets of positive integers with the property that the product of any two elements in the set increased by the unity is a square. It is shown that if the two smallest elements have the form \({ KA}^2\), \(4{ KA}^4 \pm 4 A\) for some positive integers A and K, and the third one is chosen canonically, then any such set consisting of three elements can be contained in a unique such set with four elements.
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Acknowledgements
The authors thank the referee for his/her careful reading and helpful comments. The second author is supported by Croatian Science Fund Grant Number 6422. The third author is supported by JSPS KAKENHI Grant Number 16K05079.
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Communicated by Emrah Kilic.
Dedicated to Professor Maurice Mignotte, for his influence on all of us.
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Cipu, M., Filipin, A. & Fujita, Y. An Infinite Two-Parameter Family of Diophantine Triples. Bull. Malays. Math. Sci. Soc. 43, 481–498 (2020). https://doi.org/10.1007/s40840-018-0695-9
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DOI: https://doi.org/10.1007/s40840-018-0695-9