Find all $n \in\Bbb N$ such that $2^n -1$ is divisible by $3$ and the congruence $4x^2 \equiv -1\bmod \frac{2^n-1}{3})$ has a solution.
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
36611
Algorithms for solving the discrete logarithm $a^x \equiv b\pmod{n}$ when $\gcd(a,n) \neq 1$
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
97150
Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$.
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
141531
Find the set of $n\in\Bbb Z^+$ with $M=\{n,n+1,n+2,n+3,n+4,n+5\}$ partitionable into two sets
97805
$n+1$ is a divisor of $\binom{2n} {n}$
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
80875
Congruence equation ...
105442
Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
10635
diophantine equations $x^3-2y^3=1$
107990
Does there exist an integer $x$ satisfying the following congruences?
96237
$1^2 + 2^2 + 3^2 + \cdots + (n-1)^2 \equiv 0$ mod n iff $n \equiv \pm 1$ mod 6
104965
Find $n$ such that polynomial is divisible