Geodesic
Some congruences involving inverse of binomial coefficients
Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 1, pp. 59-71

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Let $p$ be an odd prime number. In this paper, among other results, we establish some congruences involving inverse of binomial coefficients. These congruences are mainly determined modulo $p$, $p^{2}$, $p^{3}$ and $p^{4}$ in the $p$-integers ring in terms of Fermat quotients, harmonic numbers and Bernoulli numbers in a simple way. Furthermore, we extend an interesting theorem of E. Lehmer to the class of inverse binomial coefficients.
Keywords: congruence, binomial coefficient, Fermat quotient, gamma function. 
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     title = {Some congruences involving inverse of binomial coefficients},
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     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_1_a4/}
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L. Khaldi; R. Boumahdi. Some congruences involving inverse of binomial coefficients. Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 1, pp. 59-71. http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_1_a4/