On shifted primes with large prime factors and their products

摘要

In this short note, we give partial answers to two questions on shifted primes with large prime factors, posed by Luca et al. (Bull Belg Math Soc Simon Stevin 22:39-47, 2015) and by Chen and Chen (Acta Math Sin (Engl Ser) 33(3):377-382, 2017), respectively.