Výsledky vyhledávání - "Miyazaki, Takafumi"

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An application of $abc$-conjecture to a conjecture of Scott and Styer on purely exponential equations

For any fixed relatively prime positive integers $a,b$ and $c$ greater than 1, we consider the equation $a^x+b^y=c^z$ in positive integers $x,y$ and $z$. In this note, assuming the truth of $abc$-conjecture, for any fixed $c$ we prove that there is a

Externí odkaz: http://arxiv.org/abs/2407.07407

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Number of solutions to a special type of unit equations in two unknowns, III

Autor: Miyazaki, Takafumi, Pink, István

It is conjectured that for any fixed relatively prime positive integers $a,b$ and $c$ all greater than 1 there is at most one solution to the equation $a^x+b^y=c^z$ in positive integers $x,y$ and $z$, except for specific cases. We develop the methods

Externí odkaz: http://arxiv.org/abs/2403.20037

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Number of solutions to a special type of unit equations in two unknowns, II

Autor: Miyazaki, Takafumi, Pink, István

This paper contributes to the conjecture of R. Scott and R. Styer which asserts that for any fixed relatively prime positive integers $a,b$ and $c$ all greater than 1 there is at most one solution to the equation $a^x+b^y=c^z$ in positive integers $x

Externí odkaz: http://arxiv.org/abs/2205.11217

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Number of solutions to a special type of unit equations in two variables

Autor: Miyazaki, Takafumi, Pink, István

For any fixed coprime positive integers $a,b$ and $c$ with $\min\{a,b,c\}>1$, we prove that the equation $a^x+b^y=c^z$ has at most two solutions in positive integers $x,y$ and $z$, except for one specific case which exactly gives three solutions. Our

Externí odkaz: http://arxiv.org/abs/2006.15952

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