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On congruences with binomial coefficients and harmonic numbers

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Koparal, Sibel

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Elkhiri, Laid
Ömür, Neşe

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Univ Nis, Fac Sci Math

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In this paper, we obtain super congruencesSigma([(p-1)/r])(k=1) (1)(k+1)(( alpha p - 1)(k))H-k(2) (mod p(2)) and Sigma([(p-1)/r])(k=1) (1-())k k((alpha p - 1)(k))H-k(2) (mod p(2)),where r is an element of {1, 2, 3} and alpha is a p-adic integer. Also, we give new congruences involving binomial coefficients and harmonic numbers.

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Bernoulli numbers, Congruences, Harmonic numbers, Bernoulli numbers and binomial coefficients, Science & technology, Physical sciences, Mathematics, applied, Mathematics

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