The Diophantine equation $P(x)=\overset{r}{\underset{i=1}{\prod}}H_{n_i}$

Naciri proved that for any integer $k \geq 2$ , the Brocard–Ramanujan equation $n! + 1 = x^{2}$ has only finitely many integer solutions, assuming $x \pm 1$ is a $k$ -free integer or a prime power. In the present paper we prove similar statements for equations of the form $P (x) = \prod_{i = 1}^{r} H_{n_{i}}$ , where $P (x)$ is a polynomial and $H_{n_{i}}$ are divisible sequences.

The Diophantine equation $P (x) = \overset{r}{\prod_{i = 1}} H_{n_{i}}$

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The Diophantine equation $P (x) = \overset{r}{\prod_{i = 1}} H_{n_{i}}$

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The Diophantine equation P(x)=∏i=1rHniP(x)=i=1∏​r​Hni​​

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The Diophantine equation P(x)=∏i=1rHniP(x)=i=1∏​r​Hni​​

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The Diophantine equation $P (x) = \overset{r}{\prod_{i = 1}} H_{n_{i}}$

讲解博客

AI智能校验

The Diophantine equation $P (x) = \overset{r}{\prod_{i = 1}} H_{n_{i}}$

讲解博客

AI智能校验