On a conjecture of Pomerance

Details On a conjecture of Pomerance On a conjecture of Pomerance

2011-07-26

arxiv.org/abs/1107.5191v1

Mathematics

Number Theory

10 pages. Submitted to Acta Arithmetica

Scientific paper

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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