Exercise 4.2.13 (There are infinitely many integers $x$ satisfying $d(x) = n$)

Question

Given any positive integer $n$, prove that there are infinitely many integers $x$ satisfying $d(x) = n$.

Richard Ganaye · Accepted Answer

\begin{proof} 
Let $p$ be any prime number. Then $d(p^{n-1}) = n$. Since there are infinitely many prime numbers, there are also infinitely many integers $x$ satisfying $d(x) = n$.
\end{proof}

Exercise 4.2.13 (There are infinitely many integers $x$ satisfying $d(x) = n$)

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Exercise 4.2.13 (There are infinitely many integers $x$ satisfying $d(x) = n$)

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