English

Smallest totient in a residue class

Number Theory 2025-04-11 v2

Abstract

We obtain a totient analogue for Linnik's theorem in arithmetic progressions. Specifically, for any coprime pair of positive integers (m,a)(m,a) such that mm is odd, there exists nm2+o(1)n\le m^{2+o(1)} such that φ(n)amodm\varphi(n)\equiv a\,\mathrm{mod}\,{m}.

Keywords

Cite

@article{arxiv.2412.04632,
  title  = {Smallest totient in a residue class},
  author = {Abhishek Jha},
  journal= {arXiv preprint arXiv:2412.04632},
  year   = {2025}
}

Comments

To appear in Bulletin of London Mathematical Society

R2 v1 2026-06-28T20:24:56.640Z