Bounds for prime solutions of some diagonal equations. II

Liu, Ming Chit

doi:10.1090/S0002-9947-1986-0854075-3

Bounds for prime solutions of some diagonal equations. II
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Trans. Amer. Math. Soc. 297 (1986), 415-426 Request permission

Abstract:

Let ${b_j}$ and $m$ be certain integers. In this paper we obtain a bound for prime solutions ${p_j}$ of the diagonal equations of order $k,\;{b_1}p_1^k + \cdots + {b_s}p_s^k = m$. The bound obtained is ${C^{{{(\log B)}^2}}} + C|m{|^{1/k}}$ where $B = {\max _j}\{ e,|{b_j}|\}$ and $C$ are positive constants depending at most on $k$.

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