More on consecutive multiplicatively dependent triples of integers
Journal de théorie des nombres de Bordeaux, Tome 38 (2026) no. 1, pp. 179-222

In this paper, we extend recent work of the third author and Ziegler on triples of integers $(a,b,c)$, with the property that each of $(a,b,c)$, $(a+1,b+1,c+1)$ and $(a+2,b+2,c+2)$ is multiplicatively dependent, completely classifying such triples in case $a=2$. Our techniques include a variety of elementary arguments together with more involved machinery from Diophantine approximation.

Dans cet article, nous étendons le travail récent du troisième auteur et Ziegler sur les triplets d’entiers $(a,b,c)$ avec la propriété que chacun des triplets $(a,b,c)$, $(a+1,b+1,c+1)$ et $(a+2,b+2,c+2)$ est multiplicativement dépendant, en classifiant complètement ces triplets dans le cas $a=2$. Nos techniques incluent divers arguments élémentaires ainsi qu’une machinerie plus complexe issue de l’approximation diophantienne.

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DOI : 10.5802/jtnb.1359
Classification : 11N25, 11D61, 11J86
Keywords: Multiplicative dependence, Pillai’s problem, Linear forms in logarithms
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Michael A. Bennett; István Pink; Ingrid Vukusic. More on consecutive multiplicatively dependent triples of integers. Journal de théorie des nombres de Bordeaux, Tome 38 (2026) no. 1, pp. 179-222. doi: 10.5802/jtnb.1359
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