Call a natural number simple if it is not divisible by any square of a prime number (in other words it is square-free). Prove that there are infinitely many positive integers $n$ such that both $n$ and $n+1$ are simple.
Source: 2018 Latvia BW TST P16
Tags: number theory, prime numbers, number theory unsolved
Call a natural number simple if it is not divisible by any square of a prime number (in other words it is square-free). Prove that there are infinitely many positive integers $n$ such that both $n$ and $n+1$ are simple.