Show that there exists a positive integer $k$ such that $g^k=1_G$
112974
The $h-$th power of every element in a finite group of order $h$ is the identity element of the group
24181
Showing that $G$ is a group under an alternative operation.
44729
Prove $g$ is a generator if $g^q=1 \pmod p$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
107716
Show that $G$ is cyclic
46863
Show that $g$ is injective
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
67527
Proof by Induction that $3^n ≥ 1+2^n$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
2408
Show that a polynomial has at least one positive solution/root.
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
129163
Showing that every positive integer can be represented in this form
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
70066
Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
99630
For every $g\in G$ there exists an $h\in G$ such that $g = h^3$
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$