对leonetti和luca定理的改进

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2023-09-01 DOI:10.1017/s0004972723000862

Tran Nguyen Thanh Danh, Hoang Tuan Dung, Pham Viet Hung, Nguyen Dinh Kien, Nguyen AN Thinh, Khuc Dinh Toan, N. X. Tho

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引用次数: 0

摘要

Leonetti和Luca[关于移位欧拉函数的迭代]，Bull。是的。数学。Soc。已经表明，由$x_{n+2}=\phi (x_{n+1})+\phi (x_{n})+k$定义的整数序列$(x_n)_{n\geq 1}$，其中$x_1,x_2\geq 1$, $k\geq 0$和$2 \mid k$由$4^{X^{3^{k+1}}}$限定，其中$X=(3x_1+5x_2+7k)/2$。我们改进了这个结果，证明了序列$(x_n)$受$2^{2X^2+X-3}$的约束，其中$X=x_1+x_2+2k$。

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AN IMPROVEMENT TO A THEOREM OF LEONETTI AND LUCA

Leonetti and Luca [‘On the iterates of the shifted Euler’s function’, Bull. Aust. Math. Soc., to appear] have shown that the integer sequence

$(x_n)_{n\geq 1}$

defined by

$x_{n+2}=\phi (x_{n+1})+\phi (x_{n})+k$

, where

$x_1,x_2\geq 1$

$k\geq 0$

and

$2 \mid k$

, is bounded by

$4^{X^{3^{k+1}}}$

, where

$X=(3x_1+5x_2+7k)/2$

. We improve this result by showing that the sequence

$(x_n)$

is bounded by

$2^{2X^2+X-3}$

, where

$X=x_1+x_2+2k$

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society