On the largest prime factors of consecutive integers

Sur les plus grands facteurs premiers d'entiers consécutifs

Xiaodong Lü (1, 2) , Zhiwei Wang (2)

1 Yangzhou University
2 IECL - Institut Élie Cartan de Lorraine

Denote by P + (n) the largest prime factor of an integer n. One of Erdős-Turán's conjectures asserts that the asymptotic density of integers n satisfying P + (n) < P + (n + 1) is 1/2. In this paper, we prove that this density is larger than 0.2017, which improves the previous result " 0.1356 " of the second author.

Domaines: Théorie des nombres [math.NT]

Xiaodong Lü, Zhiwei Wang. On the largest prime factors of consecutive integers. 2018. ⟨hal-01797939⟩