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Smallest totient in a residue class
- Publication Year :
- 2024
-
Abstract
- We obtain a totient analogue for Linnik's theorem in arithmetic progressions. Specifically, for any coprime pair of positive integers $(m,a)$ such that $m$ is odd, there exists $n\le m^{2+o(1)}$ such that $\varphi(n)\equiv a\,\mathrm{mod}\,{m}$.
- Subjects :
- Mathematics - Number Theory
11B50, 11L40 (Primary) 11N64 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2412.04632
- Document Type :
- Working Paper