Author

Renzhang Liu

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Preprint Jul 2026

A Complete Proof for Tu-Deng Conjecture

Let $N=2^k-1$ and let $\operatorname{wt}(n)$ denote the binary Hamming weight. The Tu-Deng conjecture asserts that, for every $1\le t\le N-1$, at most $2^{k-1}$ pairs $(a,b)\in\{0,\ldots,N-1\}^2$ satisfy $a+b\equiv t\pmod N$ and $\operatorname{wt}(a)+\operatorname{wt}(b)<k$. Partial results are known. We give a complet...

Renzhang Liu, Heng-Yi Luo, Tianyuan Xie · 2 citations · ⚡1