Two different prime numbers $p$ and $q$ differ in less than $2$ times. Prove that exists two consecutive natural numbers, such that largest prime divisor of first number is $p$, and largest prime divisor of second number is $q$.
Source: St.Petersburg 2016 Grade 9 P4
Tags: number theory
Two different prime numbers $p$ and $q$ differ in less than $2$ times. Prove that exists two consecutive natural numbers, such that largest prime divisor of first number is $p$, and largest prime divisor of second number is $q$.