| 李三华,吴高翔.有关殆素数的二元丢番图不等式[J].数学年刊A辑,2021,42(2):179~188 |
| 有关殆素数的二元丢番图不等式 |
| A Binary Diophantine Inequality Involving Almost Primes |
| Received:September 07, 2019 Revised:November 20, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0015 |
| 中文关键词: 丢番图不等式, 指数和, 殆素数 |
| 英文关键词:Diophantine inequality, Exponential sum, Almost prime |
| 基金项目: |
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| 中文摘要: |
| P_r 表示最多 r 个素因子的正整数. 作者证明了, 对于任一足够大的实数 N 和 1 |
| 英文摘要: |
| Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper it is proved that for any sufficiently large real number N and 1 < c < c0, the inequality |pc + Prc ? N| < N 9 10 (1? cc0 )is solvable in a prime p and an almost-prime Pr. In particular for 1 < c < c0 = 1.03074432 · · · , the authors have r = 6.This result constitutes an improvement upon that of W. G. Zhai and X. D. Cao. |
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