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Claim. For coprime integers $p,q>1$ and every $\varepsilon>0$ there is $c=c(p,q,\varepsilon)>0$ such that every sufficiently large integer $n$ is a sum of distinct integers of the form $p^\alpha q^\beta$, each greater than $cn/(\log n)^{1+\varepsilon}$. This is the result of W.-X. Yu, On the representation of an exponential type sequence, Publ. Math. Debrecen 104 (2024), no. 1--2, 253--261, as its abstract states it; the site's commentary gives the bound in the looser form $n/(\log n)^{1+o(1)}$. The record carries the year and no day, so this page carries the first of 2024. The paper is not held, and its proof was not read.

Covers. The theorem proves the statement of Problem 246, in its corrected Statement, which takes $a,b\geq2$, in a stronger form in which every summand is large.

Depends on. No page of this wiki.

Acceptance. Refereed: Publicationes Mathematicae Debrecen, volume 104. Reviewed: the site's curator, Thomas Bloom, marks the problem PROVED and the commentary credits Yu with the result (problem page last edited 7 December 2025); the curator had no part in the result. The problem's settling result is Birch's theorem.