Let $p$ be a prime number. Find all solutions of the congruence $x^2\equiv x\pmod p$
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
80843
Find all solutions to $x^9 \equiv 25 \pmod {29}$
123441
Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)
77024
Find the number of solutions of $x^2=x\mod m$ for any integer $m$
136856
Diophantine equation with a prime number
108035
solving diophantine equations using congruences
21874
Solve $x^3+x \equiv 1 \pmod p$
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
102860
solve $3x^2 + 6x +1 \equiv 0 \pmod {19}$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
36941
If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
46028
Show that the solution for the Diophantine equation $x^2 - y^2 = N$ is unique if and only if $|N|$ or $\frac{|N|}{4}$, respectively, is $1$ or prime.
41890
How to get all solutions of $x^2 \equiv$ $a$ mod $p$?
78638
Find out all solutions of the congruence $x^2 \equiv29 \mod 5$.