Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Scott Reese"'
Autor:
Scott, Reese, Styer, Robert
We show that there are at most two solutions in positive integers $(x,y,z)$ to the equation $a^x+b^y=c^z$ for positive integers $a$, $b$, and $c$ all greater than one, where at least one of $a$, $b$, $c$ is not a power of 2, and $(\{a,b\},c) \ne (\{3
Externí odkaz:
http://arxiv.org/abs/2401.04197
Autor:
Scott, Reese, Styer, Robert
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at most two solutions in positive integers $(x,y,z)$ to the equation $a^x + b^y = c^z$. There are an infinite number of $(a,b,c)$ giving exactly two soluti
Externí odkaz:
http://arxiv.org/abs/2206.14067
Let $a$, $b$, $c$ be fixed coprime positive integers with $\min\{ a,b,c \} >1$. Let $N(a,b,c)$ denote the number of positive integer solutions $(x,y,z)$ of the equation $a^x + b^y = c^z$. We show that if $(a,b,c)$ is a triple of distinct primes for w
Externí odkaz:
http://arxiv.org/abs/2206.14032
Autor:
Scott Reese
This volume explores and calls into question certain commonly held assumptions about writing and technological advancement in the Islamic tradition. In particular, it challenges the idea that mechanical print naturally and inevitably displaces handwr
Autor:
Scott, Reese, Styer, Robert
Let $c$ be a positive odd integer and $R$ a set of $n$ primes coprime with $c$. We consider equations $X + Y = c^z$ in three integer unknowns $X$, $Y$, $z$, where $z > 0$, $Y > X > 0$, and the primes dividing $XY$ are precisely those in $R$. We consi
Externí odkaz:
http://arxiv.org/abs/2003.06689
Autor:
Scott Reese
Explores the social consequences of Britain's creation of an Indian Ocean empire that brought millions of Muslim subjects under a single political umbrella for the first time in the modern era.
Let $a$, $b$, $c$ be fixed coprime positive integers with $\min\{a,b,c\}>1$. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions $(x,y,z)$ of the ternary purely exponential diophantine equati
Externí odkaz:
http://arxiv.org/abs/1808.06557
Autor:
Scott, Reese, Styer, Robert
We consider $N$, the number of solutions $(x,y,u,v)$ to the equation $ (-1)^u r a^x + (-1)^v s b^y = c $ in nonnegative integers $x, y$ and integers $u, v \in \{0,1\}$, for given integers $a>1$, $b>1$, $c>0$, $r>0$ and $s>0$. Previous work showed tha
Externí odkaz:
http://arxiv.org/abs/1112.4547
Autor:
Scott, Reese, Styer, Robert
We improve earlier work on the title equation (where $p$ and $q$ are primes and $c$ is a positive integer) by allowing $x$ and $y$ to be zero as well as positive. Earlier work on the title equation showed that, with listed exceptions, there are at mo
Externí odkaz:
http://arxiv.org/abs/1112.4548