Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz
In this note we use some
$q$
-congruences proved by the method of ‘creative microscoping’ to prove two conjectures on supercongruences involving central binomial coefficients. In particular, we confirm the
$m=5$
case of Conjecture 1.1 of Guo [‘Some generalizations of a supercongruence of Van Hamme’, Integral Transforms Spec. Funct.28 (2017), 888–899].
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.