当前位置: X-MOL 学术Bull. Aust. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
SOLUTIONS TO A LEBESGUE–NAGELL EQUATION
Bulletin of the Australian Mathematical Society ( IF 0.7 ) Pub Date : 2021-05-24 , DOI: 10.1017/s0004972721000381
NGUYEN XUAN THO

We find all integer solutions to the equation $x^2+5^a\cdot 13^b\cdot 17^c=y^n$ with $a,\,b,\,c\geq 0$ , $n\geq 3$ , $x,\,y>0$ and $\gcd (x,\,y)=1$ . Our proof uses a deep result about primitive divisors of Lucas sequences in combination with elementary number theory and computer search.

中文翻译:

LEBESGUE-NAGELL 方程的解

我们找到方程的所有整数解$x^2+5^a\cdot 13^b\cdot 17^c=y^n$$a,\,b,\,c\geq 0$,$n\geq 3$,$x,\,y>0$$\gcd (x,\,y)=1$. 我们的证明结合了基本数论和计算机搜索,使用了关于卢卡斯序列的原始除数的深层结果。
更新日期:2021-05-24
down
wechat
bug