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- Title
AN IMPROVEMENT TO A THEOREM OF LEONETTI AND LUCA.
- Authors
DANH, TRAN NGUYEN THANH; DUNG, HOANG TUAN; HUNG, PHAM VIET; KIEN, NGUYEN DINH; THINH, NGUYEN AN; TOAN, KHUC DINH; THO, NGUYEN XUAN
- Abstract
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 $X=x_1+x_2+2k$.
- Subjects
INTEGERS; MATHEMATICS; BULLS
- Publication
Bulletin of the Australian Mathematical Society, 2024, Vol 109, Issue 3, p437
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972723000862