1 citations · 1 across the 6 of their papers we have counts for
6 papers
Handling some Diophantine equation via Euclidean algorithm and its application to purely exponential equations
Takafumi Miyazaki, Reese Scott, Robert Styer
In this paper, we use a variety of classical and new research methods for ternary exponential Diophantine equations and extensive use of computer calculations to study the conjectu…
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…
Solving an infinite number of purely exponential Diophantine equations with four terms
Takafumi Miyazaki
An important unsolved problem in Diophantine number theory is to establish a general method to effectively find all solutions to any given -unit equation with at least four term…
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…
Number of solutions to a special type of unit equations in two unknowns, III
Takafumi Miyazaki, István Pink
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…
Number of solutions to a special type of unit equations in two unknowns, II
Takafumi Miyazaki, István Pink
This paper contributes to the conjecture of R. Scott and R. Styer which asserts that for any fixed relatively prime positive integers and all greater than 1 there is at m…