Seven squares from three numbers
Number Theory
2026-04-13 v1
Abstract
We study triples {a,b,c} of distinct nonzero rational numbers such that a+1,b+1,c+1,ab+1,ac+1,bc+1 and abc+1 are all perfect squares. We prove that there exist infinitely many such triples. In contrast, we show that no triple of positive integers has this property.
Keywords
Cite
@article{arxiv.2604.08729,
title = {Seven squares from three numbers},
author = {Andrej Dujella and Matija Kazalicki and Vinko Petričević},
journal= {arXiv preprint arXiv:2604.08729},
year = {2026}
}
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5 pages