Proof of odd number of divisors of a perfect square
65581
$m$ is a perfect square iff $m$ has an odd number of divisors?
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
17660
Show that the odd prime divisors of $n^2+n+1$ are of form $6k+1$ (exclude 3)
10920
$\delta_2(n)$ the sum of the squares of the positive divisors of $n$.
44575
The sigma function (sum of divisors) multiplicative proof
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
21108
Perfect squares and modularly congruency in mod 5
74523
Proof by Cases involving divisibility
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
2771
A group has odd number of elements iff each element is a square, $a=b^2$.
41641
$(n-7)(n+7)=$ some perfect square
11967
number of subsets of even and odd
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
54359
Odd Primes Problem Proof
72666
Prime Numbers And Perfect Squares
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
101832
Proof that sum of first $n$ cubes is always a perfect square