| On a Conjecture of Golomb on Powerful Numbers |
| Received:October 27, 1987 |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1989.03.028 |
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