Author

Huixi Li

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Preprint Oct 2026

$6$ powers of $2$ in the Linnik--Goldbach problem

Linnik's approximation to Goldbach's conjecture concerns the representation of sufficiently large even integers as the sum of two primes and a bounded number of powers of two. We prove that $6$ powers of $2$ suffice unconditionally and that $5$ suffice under the GRH, improving previous works.

Hui-Xi Li, Zhi-Xin Liu · 0 citations

Preprint Jul 2026

A Romanoff-type theorem for $P_2$+{$a^a$: a$\ge$ 1}

Let $\Omega(n)$ denote the number of prime factors of $n$, counted with multiplicity, and put $P_2$={$m$ $\ge$ 1:$\Omega(m)$ $\le$ 2}. We prove that the sumset $P_2$+{$a^a$: a$\ge$ 1} has positive lower density. The proof uses the Romanoff second moment method, in the spirit of Li and Pan's theorem on $P_2$+$2^{\mathca...

Yuchen Ding, Huixi Li, Junfeng Li · 0 citations