Seven squares from three numbers

Fuente: arXiv
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Bibliographic Details
Main Authors: Dujella, Andrej, Kazalicki, Matija, Petričević, Vinko
Format: Preprint
Published: 2026
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author Dujella, Andrej
Kazalicki, Matija
Petričević, Vinko
author_facet Dujella, Andrej
Kazalicki, Matija
Petričević, Vinko
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_08729
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Seven squares from three numbers
Dujella, Andrej
Kazalicki, Matija
Petričević, Vinko
Number Theory
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.
title Seven squares from three numbers
topic Number Theory
url https://arxiv.org/abs/2604.08729