Year: 2026
Type: article
Abstract: We prove that under a necessary independence assumption, there are only finitely many integers having bounded sum-of-digits in base b1 while also having some integral power with bounded sum-of-digits in base b2 where b1 and b2 are coprime. These powers can also be effectively listed in principle. Furthermore, analogous results involving both radix and Ostrowski numeration systems have been established.
Source: Acta Arithmetica
Authors: Divyum Sharma, L. Singhal
Institution: Birla Institute of Technology and Science, Pilani
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4407123423