The Primary Pretenders
Number Theory
2016-09-07 v1
Abstract
We call a composite number q such that there exists a positive integer b with b^p == b (mod q) a prime pretender to base b. The least prime pretender to base b is the primary pretender q_b. It is shown that there are only 132 distinct primary pretenders, and that q_b is a periodic function of b whose period is the 122-digit number 19568584333460072587245340037736278982017213829337604336734362- 294738647777395483196097971852999259921329236506842360439300.
Keywords
Cite
@article{arxiv.math/0207180,
title = {The Primary Pretenders},
author = {J. H. Conway and R. K. Guy and W. A. Schneeberger and N. J. A. Sloane},
journal= {arXiv preprint arXiv:math/0207180},
year = {2016}
}
Comments
7 pages