On the number of distinct prime factors of nj+a^hk

2009/07/12 by Hao Pan, Pan, Hao
Mathematics · #Analytic Number Theory Research #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.0907.1940

Abstract

Let ω(n) denote the number of distinct prime factors of n. Then for any given K≥ 2, small ε>0 and sufficiently large (only depending on K and ε) x, there exist at least x^1-ε integers n∈[x,(1+K^-1)x] such that ω(nj± a^hk)≥(logloglog x)^1/3-ε for all 2≤ a≤ K, 1≤ j,k≤ K and 0≤ h≤ Klog x.

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