Question 164
For a positive integer $n$, let $\tau(n)$ be the number of positive divisors of $n$.
a) Find all positive integers $n$ such that $\tau(n) + 2023 = n$.
b) Prove that there exist infinitely many positive integers $k$ such that there are exactly two positive integers $n$ satisfying $\tau(kn) + 2023 = n$.
a) Find all positive integers $n$ such that $\tau(n) + 2023 = n$.
b) Prove that there exist infinitely many positive integers $k$ such that there are exactly two positive integers $n$ satisfying $\tau(kn) + 2023 = n$.