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《Journal of Nanjing University(Mathematical Biquarterly)》 2018-01
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A NEW PROOF OF THE SUN-ZAGIER CONGRUENCE

Mu Qianruo;Dpartment of Mathematical Sciences, University of Liverpool;  
In 2011, Z. W. Sun and D. Zagier obtained the following elegant congruence connecting Bell numbers with derangement numbers:(∑)(B_κ)/(-m)~κ)≡(-1)~(m-1)D_(m-1)(mod p)for any prime p and positive integer m(■) 0(mod p). In this paper we give a new proof the Sun-Zagier congruence via a combinatorial identity of R.J. Clarke and M. Sved.
【CateGory Index】: O157
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