论文标题
ABC的猜想意味着只有有限的许多S扣数字是Repunits
The abc Conjecture Implies That Only Finitely Many s-Cullen Numbers Are Repunits
论文作者
论文摘要
假设ABC的猜想具有$ε= 1/6 $，我们使用基本方法表明，除了两个已知的无限家庭外，只有有限的许多$ S $ cullen数字是对的。更准确地说，只有有限的许多积极整数$ s $，$ n $，$ b $和$ q $带有$ s，b \ geq 2 $和$ n，q \ geq 3 $ hamplesy \ [c_ {c_ {s，n} = ns^n + 1 = \ frac = \ frac {b^q -1}}
Assuming the abc conjecture with $ε=1/6$, we use elementary methods to show that only finitely many $s$-Cullen numbers are repunits, aside from two known infinite families. More precisely, only finitely many positive integers $s$, $n$, $b$, and $q$ with $s,b \geq 2$ and $n,q \geq 3$ satisfy \[C_{s,n} = ns^n + 1 = \frac{b^q -1}{b-1}.\]
