Prove $ ∀a, b, c ∈ Z,$ if $ab + ac ≡ 3$ (mod 6) then b $\not\equiv$ c (mod 6).
47232
Prove $\forall a,b,c \in \mathbb Z$, if $ab+ac\equiv 3\pmod 6$ then $b \not\equiv c \pmod 6$ by contraposition
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
151764
modular arithmetic, solving $ax + b \equiv c \pmod d$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
39779
If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
32803
Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24)
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
17519
Let $z \in\Bbb{C}^{\times}$ such that $|z^3+\frac{1}{z^3}|\leq 2$. Prove that $|z+\frac{1}{z}|\leq 2$.
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
77383
Prove that $n^3=n \text{ mod }6$ for every integer $n$.