For any prime power we obtain estimates for the quantity , the smallest positive integer such that for any integers with , and integer , the congruence
is solvable in integers , with , . Let with , and . For odd and we obtain
for some constant . Several other estimates are given for as well as for the related quantities , for primitive representations, and , for any representation.
"Waring numbers for diagonal congruences." Rocky Mountain J. Math. 50 (3) 825 - 838, June 2020. https://doi.org/10.1216/rmj.2020.50.825