about groups?

Question

if G is afinite group show that the number of nonidentity element that satesfies the equation x^5=e is multiple of 4.
" e is identity"

Answer 1

Let g be such an element.
Then g, g², g³ and g^4 also satisfy g ^5 = e.
If h is any other element such that h^5 = e, the
same is true for h. So for each such element
we have 4 nonidentity elements satisfying the relation,
and the total number of such elements must be
a multiple of 4.

Answer 2

a^5=e, a<>e, then

{a, a^2, a^3, a^4} are all different and not equal to e.

All the elements of G of order 5 are part of one of these 4 element sets, all of them disjoint. Then, the number of elements of G of order 5 is a multiple of 4.