| 关于2表为不同奇单位分数的和 |
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| 引用本文： | 边欣,李忠民. 关于2表为不同奇单位分数的和[J]. 北京联合大学学报(自然科学版), 2012, 26(3): 63-65 |
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| 作者姓名： | 边欣 李忠民 |
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| 作者单位： | 天津师范大学数学系,天津,300387;天津大学管理与经济学部,天津,300072 |
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| 摘 要： | 记m=33×5×7×11×13×17×19×23×29×31×37,本文得到2的不同奇单位分数之和的分解式:2=1/3+1/5+1/7+1/9+1/(11)+1/(13)+1/(15)+1/(17)+1/(19)+1/(21)+1/(27)+1/(29)+…+1/(954 094 903 047)。式中共有4 074个奇单位分数,单位分数的分母分别为m的除了1,23,3×11×29,3×11×23×29×37,3×13×17×19×23×29×37,m/(51),m/(33),m/(31),m/(29),m/(27),m/(23),m/(21),m/(19),m/(17),m/(15),m/(13),m/(11),m/9,m/7,m/5,m/3,m共22个因数之外的其余全部因数,最大分母为m35。
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| 关 键 词： | 单位分数 奇单位分数 分母 因数 |
On Expressing Two as Sums of Distinct Odd Unit Fractions |
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| BIAN Xin,LI Zhong-min. On Expressing Two as Sums of Distinct Odd Unit Fractions[J]. Journal of Beijing Union University, 2012, 26(3): 63-65 |
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| Authors: | BIAN Xin LI Zhong-min |
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| Affiliation: | 1.Department of Mathematics,Tianjin Normal University,Tianjin 300387,China; 2.School of Management and Economics,Tianjin University,Tianjin 300072,China) |
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| Abstract: | By denoting m=33×5×7×11×13×17×19×23×29×31×37,an expression of two as a sum of distinct odd unit fractions:2=1/3+1/5+1/7+1/9+1/(11)+1/(13)+1/(15)+1/(17)+1/(19)+1/(21)+1/(27)+1/(29)+…+1/(954 094 903 047) is obtained.There are 4074 odd unit fractions in the expansion.The denominators of unit fractions are all divisors of m except for 22 divisors 1,23,3×11×29,3×11×23×29×37,3×13×17×19×23×29×37,m/(51),m/(33),m/(31),m/(29),m/(27),m/(23),m/(21),m/(19),m/(17),m/(15),m/(13),m/(11),m/9,m/7,m/5,m/3,m,and the max denominator is m 35. |
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| Keywords: | Unit Fraction Odd Unit Fraction Denominator Divisor |
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