Can you prove that if $\mid D_n \mid = m$, where $m$ is odd, then $n$ is a perfect square.
65581
$m$ is a perfect square iff $m$ has an odd number of divisors?
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
105564
If $n$ is a positive integer greater than 1 such that $3n+1$ is perfect square, then show that $n+1$ is the sum of three perfect squares.
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
148163
Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better
134365
When is this true: If $m^2$ is a multiple of N then m is a multiple of N
114796
Direct proof that the product of odd integers is odd
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
134121
Determining all the positive integers $n$ such that $n^4+n^3+n^2+n+1$ is a perfect square.