Number Theory - Find all $n$ such that $x^2 ≡ x$ (mod $n$) for $x$ ≡ 0,1 (mod $n$) only
3563
Find all roots of $\,x^2\!\equiv x\pmod{\!900}$, i.e all idempotents in $\Bbb Z_{900}$
17176
Proof that $x^n \mod b = (x \mod b)^n$
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
13904
$p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
78638
Find out all solutions of the congruence $x^2 \equiv29 \mod 5$.
96647
Number theory: Problem involving rational numbers
149841
Find the number of integer pairs 0 ≤ a, b ≤ 100 such that a^20 ≡ b^50 (mod 101). Need help with understanding solution
142008
Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
32803
Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24)
513
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
40156
Determine all primes $p$ for which $5$ is a quadratic residue modulo $p$
38727
Modular Exponentiation and Primes
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
68635
When is $2$ a quadratic residue mod $p$?
152591
For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?