Prove that the number of divisors of a number that is a power of a natural number, is odd.
48787
A number is a perfect square if and only if it has odd number of positive divisors
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
50133
The sum of odd powered real numbers equals zero implies the numbers are inverses
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
52032
Prove that ${n^5 - n}$ is divisible by 5
103116
Prove that any odd number can be a leg in a Pythagorean Triple
97805
$n+1$ is a divisor of $\binom{2n} {n}$
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
134000
Proof by Strong Induction: $n = 2^a b,\, b\,$ odd, every natural a product of an odd and a power of 2
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
49509
A number $n$ has $12$ divisors and $d_{d_4-1} = (d_1+d_2+d_4)d_8$.
94983
Can an odd number $n$ divide $2^n-1$?
27449
Product of Divisors of some $n$ proof
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
513
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
7414
Prove that odd perfect square is congruent to $1$ modulo $8$