一个素变量混合幂丢番图不等式

牟全武, 瞿云云

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 491-500.

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数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 491-500. DOI: 10.12386/A2015sxxb0050
论文

一个素变量混合幂丢番图不等式

    牟全武1, 瞿云云2
作者信息 +

A Diophantine Inequality with Prime Variables and Mixed Power

    Quan Wu MU1, Yun Yun QU2
Author information +
文章历史 +

摘要

证明了: 设 k 是大于或等于 2 的正整数,η是任意给定的实数, λ1, λ2, λ3是非零实数, 不全同号, 并且λ12 是无理数, 则不等式 |λ1p12p23p3k+η|<(max pj)-σ 有无穷多组素数解 p1, p2, p3, 这里 σ 满足: 当 2≦k≦ 3 时, 0<σ<1/2(2k+1+1);当 4≦k≦ 5 时, 0<σ<5/(6k2k); 当 k≧ 6 时, 0<σ<20/(21k2k).

Abstract

Let k be an integer with k ≥ 2 and η be any real number. Suppose that λ1, λ2, λ3 are nonzero real numbers, not all of the same sign and λ12 is irrational. It is proved that the inequality |λ1p12p23p3k +η| < (max pj)-σ has infinitely many solutions in prime variables p1, p2, p3, where 0 < σ < 1/2(2k+1+1) for 2 ≤ k ≤ 3, 0 < σ < 5/(6k2k) for 4 ≤ k ≤ 5, and 0 < σ < 20/(21kk) for k ≥ 6.

关键词

丢番图不等式 / 混合幂 / Davenport&mdash / Heilbronn 方法

Key words

Diophantine inequality / mixed power / Davenport-Heilbronn method

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导出引用
牟全武, 瞿云云. 一个素变量混合幂丢番图不等式. 数学学报, 2015, 58(3): 491-500 https://doi.org/10.12386/A2015sxxb0050
Quan Wu MU, Yun Yun QU. A Diophantine Inequality with Prime Variables and Mixed Power. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 491-500 https://doi.org/10.12386/A2015sxxb0050

参考文献

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