| 袁平之.关于幂数问题的一个Golomb猜想[J].数学研究及应用,1989,9(3):453~456 |
| 关于幂数问题的一个Golomb猜想 |
| On a Conjecture of Golomb on Powerful Numbers |
| 投稿时间：1987-10-27 |
| DOI：10.3770/j.issn:1000-341X.1989.03.028 |
| 中文关键词: |
| 英文关键词: |
| 基金项目:国家自然科学基金资助的课题. |
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| 中文摘要: |
| 本文用Pell方程的知识,否定了Golomb猜想2°,并且证明:任意一个数m(m≠0)均可真表示为两个幂数的差,且表法无限。 |
| 英文摘要: |
| S. W.Golomb conjectured that there are infinitely many numbers of the form 2(26+1) b≥ 0 which cannot be represented as the difference of two powerful numbers. In this paper, by using some properties of Pell equation, we have disproved the conjecture, and proved.For any given number m> 0 , m have infinitely many proper representations as the difference of two powerful numbers. |
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