Apagodu, Moa Elementary proof of congruences involving sum of binomial coefficients. (English) Zbl 1428.11037 Int. J. Number Theory 14, No. 6, 1547-1557 (2018). Summary: We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients. Cited in 2 ReviewsCited in 6 Documents MSC: 11B65 Binomial coefficients; factorials; \(q\)-identities 05A10 Factorials, binomial coefficients, combinatorial functions 11A07 Congruences; primitive roots; residue systems Keywords:binomial coefficients; constant term; Laurent series; congruences Software:MultiZeilberger; CTcong.txt PDFBibTeX XMLCite \textit{M. Apagodu}, Int. J. Number Theory 14, No. 6, 1547--1557 (2018; Zbl 1428.11037) Full Text: DOI arXiv References: [1] Apagodu, M.; Zeilberger, D., Multi-variable Zeilberger and almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory, Adv. Appl. Math., 37, 139-152, (2006) · Zbl 1108.05010 [2] Apagodu, M.; Zeilberger, D., Using the “freshman’s dream” to prove combinatorial congruences, Amer. Math. Monthly, 124, 7, 597-608, (2017) · Zbl 1391.11047 [3] Chen, W. Y. C.; Hou, Q.-H.; Zeilberger, D., Automated discovery and proof of congruence theorems for partial sums of combinatorial sequences, J. Difference Eq. Appl., 22, 780-788, (2016) · Zbl 1368.11020 [4] Gessel, I., Super ballot numbers, J. Symbolic Comput., 14, 179-194, (1992) · Zbl 0754.05002 [5] Golomb, S. W., Combinatorial proof of fermat’s “little” theorem, Amer. Math. Monthly, 63, 718, (1956) [6] Pan, H.; Sun, Z., A combinatorial identity with applications to Catalan numbers, Discrete Math., 306, 16, 1921-1940, (2006) · Zbl 1221.11052 [7] Sun, Z.; Tauraso, R., On some congruences for binomial coefficients, Int. J. Number Theory, 3, 645-662, (2011) · Zbl 1247.11027 [8] Wikipedia contributors, Freshman Dream, Wikipedia, The Free Encyclopedia; http://en.wikipedia.org/wiki/Freshman’s_dream. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.