Abstract.
Let be the binomial coefficient modulo b (b prime), with if l is greater than c, and let be the sum of binomial coefficients modulo b, that is (mod b). We prove the following property: the for which the couples c, l verify and are uniformly distributed in the residue classes modulo b as n tends to infinity. The method, using the Perron-Frobenius theory, applies also to and gives a new proof of the well known result for the non-zero binomial coefficients modulo b.
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(Received 21 June 1999; in revised form 13 July 2000)
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Faure, H. On the Distribution of the Sums of Binomial Coefficients Modulo a Prime. Mh Math 131, 263–277 (2000). https://doi.org/10.1007/s006050070001
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DOI: https://doi.org/10.1007/s006050070001