Question 36
We call positive integers $n, m$ an *interesting pair* if $n \lt m$ and the greatest prime factor of $n$ is equal to the greatest prime factor of $m$.
a. For an interesting pair $n, m$, will there always exist a prime $p$ such that $n \lt p \lt m$?
b. Among the first 25 positive integers, how many don't form an interesting pair with any smaller positive integer?
a. For an interesting pair $n, m$, will there always exist a prime $p$ such that $n \lt p \lt m$?
b. Among the first 25 positive integers, how many don't form an interesting pair with any smaller positive integer?