首页|The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$

The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$

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英文摘要

In this paper, we investigate the Diophantine equation \[ (2^k - 1)(3^k - 1) = x^n \] and prove that it has no solutions in positive integers $k, x, n > 2$.

作者：Bo He、Chang Liu

作者单位：

学科分类：数学

推荐引用：Bo He,Chang Liu.The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$[EB/OL].(2025-07-26)[2025-08-16].https://arxiv.org/abs/2501.04050.点此复制

The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$

The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$

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