On repunit generalized Cullen numbers
Tom 176 / 2024
Colloquium Mathematicum 176 (2024), 177-182
MSC: Primary 11D45; Secondary 11D61
DOI: 10.4064/cm9437-10-2024
Opublikowany online: 18 November 2024
Streszczenie
Let be an integer with s\ge 2 and let R_s be the number of solutions of the equation ns^{ n}+1=(b^m-1)/(b-1) in integers b\ge 2, m\ge 3 and n\ge 2. In 2022, Alahmadi and Luca proved that R_2=0. In this paper, we prove that for any prime power p^\ell , R_{p^\ell }=0.
