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math.NT2021
Upperbound for Dimension of Hilbert Cubes contained in the Quadratic Residues of
Ali Alsetri, Xuancheng Shao
We consider the problem of bounding the dimension of Hilbert cubes in a finite field that does not contain any primitive roots. We show that the dimension of such Hi…
math.NT2021
Singmaster's conjecture in the interior of Pascal's triangle
Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao +2
Singmaster's conjecture asserts that every natural number greater than one occurs at most a bounded number of times in Pascal's triangle; that is, for any natural number …
math.NT2021★ 1 cited
A transference principle for systems of linear equations, and applications to almost twin primes
Pierre-Yves Bienvenu, Xuancheng Shao, Joni Teräväinen
The transference principle of Green and Tao enabled various authors to transfer Szemerédi's theorem on long arithmetic progressions in dense sets to various sparse sets of integers…