$(\forall n \in \mathbb{Z}):n^{3} \equiv n$ (mod $6$)
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
60268
$\textit{Why}$ the cases in 4 $\nmid n^2 - 3?$ (bases cases in modular induction)
68915
What are the units in $\mathbb{Z}[\root 3 \of 2]$?
124995
$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
1895
How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$
80365
Prove that $n$ is divisible by $6$
27704
Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$
85941
Proof by induction that $n^3 - n$ is divisible by $6$
146851
Prove that $-3$ is a quadratic residue mod an odd prime $>3$ if and only if $p$ is of the form of $6n+1$
61860
Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.
130104
Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent)
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$