Modular Arithmetic: Proofs
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
118955
Specific steps in applying the Chinese Remainder Theorem to solve modular problem splitting modulus
152231
Computing the product of p/(p - 2) over the odd primes
17176
Proof that $x^n \mod b = (x \mod b)^n$
35313
Proof of Euclid's Lemma
129381
Modular equation problem
99815
Dividing versus multiplying by inverse in modular arithmetic
21476
Modular Exponentiation 3^5^7
30045
Solving linear congruences by hand: modular fractions and inverses
16700
Modular reduction of fractions
141704
Fractional exponentiation in modular arithmetic
49938
Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
136947
Simple Mersenne prime divisibility proofs
65983
Combinatorial proof of binomial coefficient summation identity