MathDB

Let

m

and

n

be positive integers with

\gcd(m, n) = 1

, and let

a_k = \left\lfloor \frac{mk}{n} \right\rfloor - \left\lfloor \frac{m(k-1)}{n} \right\rfloor

for

k = 1, 2, \dots, n

. Suppose that

g

and

h

are elements in a group

G

and that

gh^{a_1} gh^{a_2} \cdots gh^{a_n} = e,

where

e

is the identity element. Show that

gh = hg

. (As usual,

\lfloor x \rfloor

denotes the greatest integer less than or equal to

x

A4