For which odd positive integer $n$, is it true that $−1$ is not a positive power of $2$ modulo $n$? [request for more extensive results]
52542
For which odd positive integer $n$ , is it true that $-1$ is not a positive power of $2$ modulo $n$?
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
60780
Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.
96097
Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.
16660
Prove that any positive number has an $n$th root
148796
Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
107990
Does there exist an integer $x$ satisfying the following congruences?
10920
$\delta_2(n)$ the sum of the squares of the positive divisors of $n$.
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
4140
Fermat's Last Theorem with negative exponent
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
45672
Even/Odd Binomial Coefficients
77564
How to prove for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$?
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
96326
Number of $q$-th residues modulo $n$