We establish a q-analogue of Sun–Zhao's congruence on harmonic sums. Based on this q-
congruence and a q-series identity, we prove a congruence conjecture on sums of central q …

Let p> 3 be a prime. A p-adic congruence is called a super congruence if it happens to hold
modulo some higher power of p. The topic of super congruences is related to many fields …

Let p be a prime and let a be a positive integer. In this paper we determine [Formula: see
text] and∑ k= 1p− 1 (2kk+ d)/(kmk− 1) modulo p for all d= 0,…, pa, where m is any integer …

It is known that In this paper we obtain their p-adic analogues such as where p> 3 is a prime
and E0, E1, E2,… are Euler numbers. Besides these, we also deduce some other …

Based on a q-congruence of the author and Petrov, we set up a q-analogue of Sun–
Tauraso's congruence for sums of Catalan numbers, which extends a q-congruence due to …

Let p be an odd prime and let a, m∈ ℤ with a> 0 and p∤ m. In this paper we determine Σ k=
0 pa− 1 (2 k k+ d)/mk mod p 2 for d 0, 1; for example, ∑ k= 0^ p^ a-1\left (≡\left (m^ 2-4m p …

We collect here 100 open conjectures on congruences made by the author, some of which
have never been published. This is a new edition of the author's preprint arXiv: 0911.5665 …

Via symbolic computation we deduce 97 new type series for powers of $\pi $ related to
Ramanujan-type series. Here are three typical examples: $$\sum_ {k= 0}^\infty\frac {P …

In this paper we study some sophisticated supercongruences involving dual sequences. For
n= 0, 1, 2,… define dn (x)=∑ k= 0 n (nk)(xk) 2 k and sn (x)=∑ k= 0 n (nk)(xk)(x+ kk)=∑ k= 0 …

q-Analogs of some congruences involving Catalan numbers Page 1 Advances in Applied
Mathematics 48 (2012) 603–614 Contents lists available at SciVerse ScienceDirect Advances in …