Waringʹs number mod m Original Research Article

Let p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer is a sum of s kth powers image. We establish γ(k,pn)less-than-or-equals, slant[k/2]+2 and image provided that k is not divisible by (p−1)/2. Next, let t=(p−1)/(p−1,k), and q be any positive integer. We show that if phi(t)greater-or-equal, slantedq then γ(k,pn)less-than-or-equals, slantc(q)k1/q for some constant c(q). 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.