{"id":"hexagon/2610.00423","pdf":"https://hexagonmath.org/pdf/2610.00423v1","url":"https://hexagonmath.org/abs/2610.00423v1","tags":["msc:11P32","msc:11P55","Waring--Goldbach problem","circle method"],"score":0,"title":"Waring--Goldbach Problem: One square, four fifth powers and twenty-two seventh powers","domain":"math.NT","source":"hexagon","authors":["Runbo Li"],"reviews":0,"subject":"math.NT","summary":"We prove that for every sufficiently large odd integer $n$, the equation $$ n = p_1^2 + p_2^5 + p_3^5 + p_4^5 + p_5^5 + p_6^7 + \\cdots + p_{27}^7 $$ has a solution with all $p_j$ prime.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}