Anderson, Theresa C.Hu, BingyangLiu, Yu-RuTalmage, Alan2023-10-032023-10-032023http://hdl.handle.net/10012/20011Let A be an ellipsephic set which satis es digital restrictions in a given base. Using the method developed by Hughes and Wooley, we bound the number of integer solutions to the system of equations X2 i=1 􀀀 x3i 􀀀 y3 i = X5 i=3 􀀀 x3i 􀀀 y3 i X2 i=1 (xi 􀀀 yi) = X5 i=3 (xi 􀀀 yi); with x; y 2 A5. The fact that ellipsephic sets with small digit sumsets have fewer solutions of linear equations allows us to improve the general bounds obtained by Hughes andWooley and also the corresponding e cient congruencing estimates. We also generalize our result from the curve (x; x3) to (x; (x)), where is a polynomial with integer coe cients and deg( ) 3.enmean value estimatesellipsephic setsKdV-like equationsPreprint