设k,n为非负整数, S(n,k)表示第二类Stirling数.本文研究了 S(n,k)模 2 的方幂的同余式,首先给出了一类二项式系数模 2 的同余式, 然后利用上述结果得到了S(n,a2m+b)模2m的同余式.其表达式均由简单二项式系数组成, 其中m≥3, b=0,1,2.这些结果改进了Chan和Manna的结果.
Abstract
Let k and n be nonnegative integers.In this paper, we investigate the congruences for the Stirling numbers of the second kind S(n,k) modulo powers of 2.We first give a congruence for some certain binomial coefficients modulo 2.Using this result we then establish the congruences for S(n,a2m+b) modulo 2m, and express them in terms of binomial coefficients, where m ≥ 3, b= 0, 1, 2.These strengthen the results obtained by Chan and Manna.
关键词
同余式 /
第二类Stirling数 /
二项式系数
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Key words
congruence /
Stirling numbers of the second kind /
binomial coefficient
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参考文献
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