Need help finding the flaw to the proof that $(a+b)\mathrm {mod} m = a\mathrm {mod} m + b \mathrm {mod} m $
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
131905
Proof for exponentiation in modular arithmetic
55680
The relationship of ${\frak m+m=m}$ to AC
127816
Number theory proof mod p
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
154822
Properties of the composition law $a @ b= ab + b + a$ on the real numbers
103499
$x^2 \equiv a \mod p$, $\ x^2 \equiv b \mod p$, and $x^2 \equiv ab \mod p$, prove either all three are solvable or exactly one
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
17176
Proof that $x^n \mod b = (x \mod b)^n$
11989
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
1002
Where is the flaw in this "proof" that 1=2? (Derivative of repeated addition)
140167
Proving $A+A'B=A+B$ without truth tables
92518
mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$