A Problem In Elementary Number Theory

The main result of this paper is the following:Let p be an odd prime.Let a1,a2,…,an be the integers each of which is relatively prime to p.And let li(1≤i≤p-1)be the number of these at(1≤t≤n)which are congruent to i modulo p.Then the necessary and sufficient condition of a1,a2,…,an satisfy the congruence a1k+a2k+…+ank≡0(mod p),k=1,2,…,p-2 is that li are pairwise congruent modulo p for i=1,2,…,p-1.