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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
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$x^2+5^a\cdot 13^b\cdot 17^c=y^n$ 和$a,\,b,\,c\geq 0$ ,$n\geq 3$ ,$x,\,y>0$ 和$\gcd (x,\,y)=1$ . 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
中文翻译:
LEBESGUE-NAGELL 方程的解
我们找到方程的所有整数解