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| ON THE DIOPHANTINE EQUATION $\[\sum\limits_{i = 0}^k {\frac{1}{{{x_i}}}} = \frac{a}{n}\]$ |
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Citation： |
Shen Zun.ON THE DIOPHANTINE EQUATION $\[\sum\limits_{i = 0}^k {\frac{1}{{{x_i}}}} = \frac{a}{n}\]$[J].Chinese Annals of Mathematics B,1986,7(2):213~220 |
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Net amount： 762 |
Authors： |
Shen Zun; |
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| Abstract： |
In this paper,, the author proves the following result:
Let $\[{E_{a,k}}(N)\]$ denote the number of natural numbers $\[n \le N\]$ for which equation
$$\[\sum\limits_{i = 0}^k {\frac{1}{{{x_i}}}} = \frac{a}{n}\]$$
is insolable in positive integers $\[{x_i}(i = 0,1, \cdots ,k)\]$.Then
$$\[{E_{a,k}}(N) \ll N\exp \{ - C{(\log N)^{1 - \frac{1}{{k + 1}}}}\} \]$$
where the implied constant depends on a and K. |
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