6 citations · 10 across the 10 of their papers we have counts for
10 papers
A combinatorial identity with application to Catalan numbers
Hao Pan, Zhi-Wei Sun
By a very simple argument, we prove that if are nonnegative integers then $$\sum_{k=0}^l(-1)^{m-k}\binom{l}{k}\binom{m-k}{n}\binom{2k}{k-2l+m} =\sum_{k=0}^l\binom{l}{k}\bin…
Arithmetic properties of q-Fibonacci numbers and q-Pell numbers
Hao Pan
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.
A congruence involving products of -binomial coefficients
Hao Pan, Hui-Qin Cao
In this paper we establish a -analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.
A q-analogue of Lehmer's congruence
Hao Pan
We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.
A q-analogue of Wolstenholme's harmonic series congruence
Ling-Ling Shi, Hao Pan
We establish a q-analogue of Wolstenholme's harmonic series congruence.
A sharp result on m-covers
Hao Pan, Zhi-Wei Sun
Let A={a_s+n_sZ}_{s=1}^k be a finite system of arithmetic sequences which forms an m-cover of Z (i.e., every integer belongs at least to m members of A). In this paper we show the…