Bo He

collaborators

2 papers

math.NT2026

The diophantine equation $(2^{k} - 1) (b^{k} - 1) = y^{q}$

Chang Liu, Bo He

In this paper, we consider the exponential Diophantine equation $ (2^k-1)(b^k-1)=y^q $ with $k \geq 2$ , odd integer $b$ and an odd prime exponent $q$ and obtain effective upper bou…

math.NT2025

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

Bo He, Chang Liu

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 $k, x, n > 2$ .

The diophantine equation (2k−1)(bk−1)=yq

The diophantine equation (2k−1)(3k−1)=xn

The diophantine equation $(2^{k} - 1) (b^{k} - 1) = y^{q}$

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