Let n⩾3 be an integer and a1,a2,…,an be pairwise distinct positive real numbers with the property that there exists a permutation b1,b2,…,bn of these numbers such thatb1a1=b2a2=⋯=bn−1an−1=1.Prove that there exist a,b>0 such that {a1,a2,…,an}={ab,ab2,…,abn}.Cristi Săvescu