Question 6
For a positive integer $n$, let $\tau(n)$ be the number of its positive divisors.
(a) Solve $\tau(n)+2023=n$ in positive integers $n$.
(b) Prove that there are infinitely many positive integers $k$ for which exactly two positive integers $n$ satisfy $\tau(kn)+2023=n$.
(a) Solve $\tau(n)+2023=n$ in positive integers $n$.
(b) Prove that there are infinitely many positive integers $k$ for which exactly two positive integers $n$ satisfy $\tau(kn)+2023=n$.