English

Average liar count for degree-2 Frobenius pseudoprimes

Number Theory 2020-04-07 v2

Abstract

In this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham, generalizing arguments of Erd\H{o}s and Pomerance, and Monier. These bounds are provided for both Jacobi symbol plus and minus cases, providing evidence for the existence of several challenge pseudoprimes.

Cite

@article{arxiv.1707.05002,
  title  = {Average liar count for degree-2 Frobenius pseudoprimes},
  author = {Andrew Fiori and Andrew Shallue},
  journal= {arXiv preprint arXiv:1707.05002},
  year   = {2020}
}

Comments

19 pages, published in Mathematics of Computation, revised version fixes typos and made a minor correction to the proof of Lemma 18 (result remains unchanged)

R2 v1 2026-06-22T20:48:35.112Z