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# On shifted primes with large prime factors and their products

## Resumen

We estimate from below the lower density of the set of prime numbers p such that p1 has a prime factor of size at least $p^c$, where 1/4≤c≤1/2. We also establish upper and lower bounds on the counting function of the set of positive integers n≤x with exactly k prime factors, counted with or without multiplicity, such that the largest prime factor of gcd(p−1:pn) exceeds $n^{1/2k}$.

Autores: Luca, F., Menares, R., Pizarro-Madariaga, A.

Journal: Bulletin of the Belgian Mathematical Society Simon Stevin

Journal Volume: 22

Journal Issue: 1

Journal Page: 39-47

Tipo de publicación: ISI

Fecha de publicación: 2015

Topics: Shifted primes, Sieve

DOI:

URL de la publicación: http://projecteuclid.org/euclid.bbms/1426856856

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