On the Residues of Binomial Coefficients and Their Products Modulo Prime Powers |
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| Authors: | Tian Xin Cai Andrew Granville |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China E-mail: txcai@mail.hz.zj.cn, CN;(2) Department of Mathematics, University of Georgia, Athens, GA 30602, USA E-mail: andrew@sophie.math.uga.edu, US |
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| Abstract: | In this paper, we show several arithmetic properties on the residues of binomial coefficients and their products modulo prime
powers, e.g.,
for any distinct odd primes p and q. Meanwhile, we discuss the connections with the prime recognitions.
Received November 5, 1998, Accepted December 7, 2000. |
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| Keywords: | Binomial coefficients Bernoulli numbers Recognizing primes |
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