English

A note on square totients

Number Theory 2015-07-23 v1

Abstract

A well-known conjecture asserts that there are infinitely many primes pp for which p1p - 1 is a perfect square. We obtain upper and lower bounds of matching order on the number of pairs of distinct primes p,qxp,q \le x for which (p1)(q1)(p - 1)(q - 1) is a perfect square.

Keywords

Cite

@article{arxiv.1410.8109,
  title  = {A note on square totients},
  author = {Tristan Freiberg and Carl Pomerance},
  journal= {arXiv preprint arXiv:1410.8109},
  year   = {2015}
}
R2 v1 2026-06-22T06:40:43.722Z