Zhi-Wei Sun

activity

20032009

most citedVarious congruences involving binomial coefficients and higher-order Catalan numbers

11 citations · 37 across the 33 of their papers we have counts for

collaborators

Showing 2009Show all

4 papers · 1 filter

math.NT2009

Some q-congruences related to 3-adic valuations

Hao Pan, Zhi-Wei Sun

In 1992 Strauss, Shallit and Zagier proved that for any positive integer $a$ we have $k = 0 \sum 3^{a} - 1 (k 2 k) = 0 (m o d 3^{2 a})$ and furthermore $$3^{-2a}}\sum_{k=0}^{3^a-1}…

math.NT2009★ 11 cited

Various congruences involving binomial coefficients and higher-order Catalan numbers

Zhi-Wei Sun

Let $p$ be a prime and let $a$ be a positive integer. In this paper we investigate $\sum_{k = 0}^{p^{a} - 1} (( [) h + 1) k, k + d] / m^{k}$ modulo a prime $p$ , where $d$ and $m$ are integers wit…

math.NT2009★ 6 cited

Some congruences for the second-order Catalan numbers

Li-Lu Zhao, Hao Pan, Zhi-Wei Sun

Let p be any odd prime. We mainly show that $k = 1 \sum p - 1 bin o mia l (3 k, k) * 2^{k} / k = 0 (m o d p)$ and $k = 1 \sum p - 1 2^{k - 1} C_{k}^{(2)} = (- 1)^{(p - 1) /2} - 1 (m o d p),$ where $C_k^{(2)}=b…

math.NT2009

Mixed sums of primes and other terms

Zhi-Wei Sun

In this paper we study mixed sums of primes and linear recurrences. We show that if m=2(mod 4) and m+1 is a prime then $(m^{2^{n} - 1} - 1) / (m - 1) \neq = m^{n} + p^{a}$ for any n=3,4,... and prime…