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For any integer n ≥ 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p ≤ x with P(p−1)… Click to show full abstract
For any integer n ≥ 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p ≤ x with P(p−1) ≥ pc is more than (1−c+o(1))π(x) for 0 < c < 1/2. This extends a recent result of Luca, Menares and Madariaga for 1/4 ≤ c ≤ 1/2. We also pose two conjectures for further research.
Keywords:
shifted primes;
largest prime;
factor shifted;
prime factor
Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2017
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Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!