Back to Search
Start Over
Consecutive tuples of multiplicatively dependent integers.
- Source :
-
Journal of Number Theory . Jul2022, Vol. 236, p280-307. 28p. - Publication Year :
- 2022
-
Abstract
- This paper is concerned with the existence of consecutive pairs and consecutive triples of multiplicatively dependent integers. A theorem by LeVeque on Pillai's equation implies that the only consecutive pairs of multiplicatively dependent integers larger than 1 are (2 , 8) and (3 , 9). For triples, we prove the following theorem: If a ∉ { 2 , 8 } is a fixed integer larger than 1, then there are only finitely many triples (a , b , c) of pairwise distinct integers larger than 1 such that (a , b , c) , (a + 1 , b + 1 , c + 1) and (a + 2 , b + 2 , c + 2) are each multiplicatively dependent. Moreover, these triples can be determined effectively. [ABSTRACT FROM AUTHOR]
- Subjects :
- *INTEGERS
*EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 236
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 155815476
- Full Text :
- https://doi.org/10.1016/j.jnt.2021.07.021