Semi-automated proof of supercongruences on partial sums of hypergeometric series

Some supercongruences arising from symbolic summation

“…We also need some combinatorial identities, which are discovered and proved by symbolic summation package Sigma developed by Schneider [11]. One can refer to [9] for the same approach to finding and proving identities of this type. Lemma 2.4 For any positive integer n, we have n k=0 (6k + 1)…”

Proof of Two Conjectures on Supercongruences Involving Central Binomial coefficients

“…Proofs of (1.4) and (1.5). The second author [3] also proved the following qcongruences: for odd n > 1, modulo [n] 8) where M = (n + 1)/2 or n − 1. Letting q → q −1 in (2.8) and multiplying both sides by…”

“…The second author [2] proved that (1.2) is true modulo p 3 for r = 1 and primes p satisfying some congruence conditions. Liu [8] gave a proof of (1.2) for the complete r = 1 case. Hou et al [7] proved [2, Conjecture 1.1] for r = 1.…”

Proof of Sun's supercongruence involving Catalan numbers

“…On the other hand, (3.2) can be discovered and proved by symbolic summation package Sigma due to Schneider [13]. One can refer to [8] for the same approach to finding and proving identities of this type.…”