Problems(1)
Let m and n be positive integers with gcd(m,n)=1, and let
ak=⌊nmk⌋−⌊nm(k−1)⌋
for k=1,2,…,n. Suppose that g and h are elements in a group G and that
gha1gha2⋯ghan=e,
where e is the identity element. Show that gh=hg. (As usual, ⌊x⌋ denotes the greatest integer less than or equal to x.) PutnamPutnam 2018