English

On the difference in values of the Euler totient function near prime arguments

Number Theory 2021-02-05 v2

Abstract

We prove unconditionally that for each 1\ell \geq 1, the difference ϕ(p)ϕ(p+)\phi(p-\ell) - \phi(p+\ell) is positive for 50%50\% of odd primes pp and negative for 50%50\%.

Cite

@article{arxiv.1706.00392,
  title  = {On the difference in values of the Euler totient function near prime arguments},
  author = {Stephan Ramon Garcia and Florian Luca},
  journal= {arXiv preprint arXiv:1706.00392},
  year   = {2021}
}

Comments

21 pages; to appear in "Irregularities in the Distribution of Prime Numbers" (edited by M. Rassias, J. Pintz), Springer

R2 v1 2026-06-22T20:06:37.378Z