Xiang-Zi Meng

most citedProof of a conjectural supercongruence

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math.NT2016

Sums of four polygonal numbers with coefficients

Xiang-Zi Meng, Zhi-Wei Sun

Let $m \geq 3$ be an integer. The polygonal numbers of order $m + 2$ are given by $p_{m + 2} (n) = m (2 n) + n$ $(n = 0, 1, 2, \dots)$ . A famous claim of Fermat proved by Cauchy asserts that ea…

math.NT2015★ 1 cited

Proof of a conjectural supercongruence

Xiang-Zi Meng, Zhi-Wei Sun

Let $m > 2$ and $q > 0$ be integers with $m$ even or $q$ odd. We show the supercongruence $k = 0 \sum p - 1 (- 1)^{k m} (k p / m - q)^{m} \equiv 0 (mod p^{3}) .$ for any prime $p > m q$ . This c…