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math.NT — Number Theory

Waring--Goldbach Problem: One square, four fifth powers and twenty-two seventh powers

Contributed by Runbo Li

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.

Primarily human-written textHuman understanding: all partsWaring--Goldbach problemcircle method

Oct 21, 2026PDF ↗View work →

hexagon:2610.00422v1

math.NT — Number Theory

Waring--Goldbach Problem: One square, four fifth powers and fifteen sixth powers

Contributed by Runbo Li

We prove that for every sufficiently large even integer $n$ , the equation $$ n = p_1^2 + p_2^5 + p_3^5 + p_4^5 + p_5^5 + p_6^6 + \cdots + p_{20}^6 $$ has a solution with all $p_j$ prime.

Primarily human-written textHuman understanding: all partsWaring--Goldbach problemcircle method

Oct 21, 2026PDF ↗View work →

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