6 papers · 1 filter
Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields
Hai-Liang Wu, He-Xia Ni
Let be a nonconstant polynomial with nonzero discriminant and let be an integer. Inspired by the work of Alon and Bourgain, for sufficiently large pr…
On the Burgess bound and Pythagorean triples involving primitive roots
Hai-Liang Wu, He-Xia Ni
By combining the recent results of Pierce and Xu on the higher-dimensional Burgess bound with the classical one-dimensional Burgess bound, we prove that for any sufficiently large…
Supercongruences Arising from Truncated Appell Series
He-Xia Ni
In recent years, both Appell series and truncated Appell series have garnered significant research interest among scholars. In this paper, we investigate the congruence properties…
A supercongruence related to Whipple's formula and Dwork's dash operation
Chen Wang, He-Xia Ni
We establish a parametric supercongruence related to Whipple's formula and Dwork's dash operation. As a typical consequence, we obtain the following result: for any prime…
The Pell sequence and cyclotomic matrices involving squares over finite fields
Hai-Liang Wu, Li-Yuan Wang, He-Xia Ni
In this paper, by some arithmetic properties of the Pell sequence and some -adic tools, we study certain cyclotomic matrices involving squares over finite fields. For example, l…
On a generalization of R. Chapman's "evil determinant"
Li-Yuan Wang, Hai-Liang Wu, He-Xia Ni
Let be an odd prime and be an indeterminate. Recently, Z.-W. Sun proposed the following conjecture: $$\det\left[x+\left(\frac{j-i}{p}\right)\right]_{0\le i,j\le \frac{p-1}{…