If $u\equiv 1$ mod $m$ and $n$ any natural number $\neq$ char$(K)$, then $u$ is a $n$-th power in $K$.
124472
Elements with infinite roots in $p$-adic integers
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
24820
Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
14403
If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
124279
$g^k$ is a primitive element modulo $m$ iff $\gcd (k,\varphi(m))=1$
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
144732
If $[G:H]=n$, then $g^{n!}\in H$ for all $g\in G$.
127843
Prove that, for any natural number $k$ $\exists m \in M $ s.t i) $m$ has exactly $k$ $1$'s, an
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
84733
Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$