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math.NT2016
Proof of a recent conjecture of Z.-W. Sun
Song Guo, Victor J. W. Guo
The polynomials are defined by \begin{align*} d_n(x) &= \sum_{k=0}^n{n\choose k}{x\choose k}2^k. \end{align*} We prove that, for any prime , the following congruences h…
math.NT2008★ 1 cited
A variant of Tao's method with application to restricted sumsets
Song Guo, Zhi-Wei Sun
In this paper, we develop Terence Tao's harmonic analysis method and apply it to restricted sumsets. The well known Cauchy-Davenport theorem asserts that if and are nonempt…
math.NT2004
On odd covering systems with distinct moduli
Song Guo, Zhi-Wei Sun
A famous unsolved conjecture of P. Erdos and J. L. Selfridge states that there does not exist a covering system {a_s(mod n_s)}_{s=1}^k with the moduli n_1,...,n_k odd, distinct and…