On a conjecture of Pomerance
Number Theory
2011-07-27 v1
Abstract
We say that k is a P-integer if the first phi(k) primes coprime to k form a reduced residue system modulo k. In 1980 Pomerance proved the finiteness of the set of P-integers and conjectured that 30 is the largest P-integer. We prove the conjecture assuming the Riemann Hypothesis. We further prove that there is no P-integer between 30 and 10^11 and none above 10^3500.
Keywords
Cite
@article{arxiv.1107.5191,
title = {On a conjecture of Pomerance},
author = {L. Hajdu and N. Saradha and R. Tijdeman},
journal= {arXiv preprint arXiv:1107.5191},
year = {2011}
}
Comments
10 pages. Submitted to Acta Arithmetica