Waring's number mod m

Abstract: Let p be an odd prime and be the smallest positive integer s such that every integer is a sum of s kth powers . We establish and provided that k is not divisible by . Next, let , and q be any positive integer. We show that if then for some constant . These results generalize results known for the case of prime moduli. Video abstract: For a video summary of this paper, please visit http://www.youtube.com/watch?v=zpHYhwL1kD0. [Copyright &y& Elsevier]