Prove that if a ≡ b mod m and c ≡ d mod m, then ac ≡ bd mod m.
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
141369
If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
11342
Show that conguence $\bmod m\,$ is an equivalence relation
71299
Prove that $\frac{a}{b} < \frac{a+c}{b+d} <\frac{ c}{d}$
11989
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
127816
Number theory proof mod p
151764
modular arithmetic, solving $ax + b \equiv c \pmod d$?