Prove a modular equation
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
41673
Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
75318
How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4?
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
38727
Modular Exponentiation and Primes
150446
Quadratic Modular Arithmetic
51858
Showing $\gcd(2^m-1,2^n+1)=1$
56803
Finding solutions to congruence equations
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
113481
Modular Arithmetic - Find the Square Root
102234
Show $a^p \equiv a \mod 2p$
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
119628
Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$
17176
Proof that $x^n \mod b = (x \mod b)^n$
131905
Proof for exponentiation in modular arithmetic