Existence of $n$ such that $a^n=a$ for all $a$ in $Z_m$
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$
59535
Prove that there exists such a set of $n$ positive integers
135018
Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
104274
Express $C$ interms of the sets $A_n$
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
48127
Are there infinitely many $A\in \mathbb{C}^{2 \times 2}$ satisfying $A^3 = A$?
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
158364
Are there uncountably many $A\in M_3 (\mathbb {R})$ such that $A^8=I $?
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group