| 自然数集的泛可加划分 |
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| 引用本文： | 朱平天.自然数集的泛可加划分[J].南京师大学报,1990,13(2):1-5. |
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| 作者姓名： | 朱平天 |
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| 作者单位： | 南京师大数学系 |
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| 摘 要： | 本文对于由递推公式:u_m=u_(m-2)+u_(m-1),m≥3,初始值:u_1=a≥1,u_2=b≥1,所确定的递推自然数列,证明了下列结论:若d=(a,b)是奇数,且当a>b时,2|ab,则自然数集N的泛可加划分的个数为2(d-1)/2。若a>b且a、b的奇偶性相同,则N的泛可加划分不存在。
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| 关 键 词： | 自然数集 泛U－划分 互素U－划分 |
ON UNIVERSAL ADDITIVE PARTITIONS OF THE SET OF NATURAL NUMBERS |
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| Zhu Pingtian.ON UNIVERSAL ADDITIVE PARTITIONS OF THE SET OF NATURAL NUMBERS[J].Journal of Nanjing Normal University(Natural Science Edition),1990,13(2):1-5. |
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| Authors: | Zhu Pingtian |
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| Institution: | Department of Mathematics |
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| Abstract: | Consider a recurrence sequence of natural number U = {u_m},u_m=u_(m-2)+u_(m-1),m>3,u_1 = a >1,u_2=b>1. We show that if dffi (a,b) is a odd number and 2|ab whena> b, then the number of universal additive partitions of the set of natural number is exactly 2(d-1)/2 if a > b and a and b are same parity, then such partition cannot exist. |
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| Keywords: | Universal U-partition Relatively prime U-partition |
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