2 papers
math.NT2025
Purely exponential Diophantine equations with four terms of consecutive bases: contribution to Skolem's conjecture
Maohua Le, Takafumi Miyazaki
We study purely exponential Diophantine equations with four terms of consecutive bases. Notably, we prove that all solutions to the equation \[ n^x=(n+1)^y+(n+2)^z+(n+3)^w \] in po…
math.NT2024
General sharp bounds for the number of solutions to purely exponential equations with three terms
Maohua Le, Takafumi Miyazaki
It is conjectured that for any fixed relatively prime positive integers and all greater than 1 there is at most one solution to the equation in positive int…