In a finite group, show that the number of nonidentity elements that satisfy the equation $x^5=e$ is a multiple of 4.
114379
Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
15000
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group
20705
On equations $m^2+1=5^n$
127603
If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$
44484
Combinatorial identity $i{n \choose i } =n {n-1 \choose i - 1}$
65613
$G$ is a finite group and $T$ an automorphism of $G$ such that $T$ sends more than $\frac{3}{4}|G|$ elements to their inverse.
2104
Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
27141
Combinatorics identity question
81354
The product of all the elements of a finite abelian group
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
15341
Non-abelian finite group in which more than half of the elements have order $2$
145254
$G$ be a non-nilpotent and supersoluble finite group.
61483
Prove the following identity combinatorially
102971
Product of all elements of a finite group with an unique element of order 2
28676
Is a finite group uniquely determined by the orders of its elements?
73743
Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$