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.