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arXiv · 1107.5191

On a conjecture of Pomerance

L. Hajdu·N. Saradha·R. Tijdeman
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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.

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L. Hajdu, N. Saradha, R. Tijdeman. 2011-07-26. On a conjecture of Pomerance. https://arxiv.org/abs/1107.5191

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