Analogues of the binomial coefficient theorems of Gauss and Jacobi
2016 ◽
Vol 12
(08)
◽
pp. 2125-2145
Keyword(s):
The theorems of Gauss and Jacobi that give modulo [Formula: see text] evaluations of certain central binomial coefficients have been extended, since the 1980s, to more classes of binomial coefficients and to congruences modulo [Formula: see text]. In this paper, we further extend these results to congruences modulo [Formula: see text]. In the process, we prove congruences to arbitrarily high powers of [Formula: see text] for certain quotients of Gauss factorials that resemble binomial coefficients and are related to Morita's [Formula: see text]-adic gamma function. These congruences are of a simple form and involve Catalan numbers as coefficients.
2016 ◽
Vol 60
(2)
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pp. 527-543
2009 ◽
Vol 93
(528)
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pp. 449-455
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2012 ◽
Vol 93
(1-2)
◽
pp. 189-201
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2010 ◽
Vol 53
(9)
◽
pp. 2473-2488
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2015 ◽
Vol DMTCS Proceedings, 27th...
(Proceedings)
◽
2019 ◽
Vol 11
(02)
◽
pp. 1950017
2015 ◽
Vol 3
(4)
◽
pp. 140
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