关于不定方程(an-1)(bn-1)= X2解的研究
On the Diophantine Equation(an-1)(bn-1)= X2

作者: 吴磊 * , 李召君 :;

关键词: 不定方程Legendre符号Diophantine Equation Legendre Symbol

摘要: 2002年,F. Luca和P. G. Walsh研究了不定方程(an-1)(bn-1)= X2 在2≤b≤a≤100范围内的情况(除69种例外)。在本文中,我们研究了其中的两种例外。也就是,我们考虑的是不定方程(an-1)(bn-1)= X2 在(a,b)=(33,3)(33,9)时解的情况。

Abstract: In 2002, F. Luca and P. G. Walsh studied the diophantine equations of the form(an-1)(bn-1)= X2 , for all in the range with sixty-nine exceptions. In this paper, we study two of the exceptions. In fact, we consider the equations of the form (an-1)(bn-1)= X2 , with (a,b)=(33,3)(33,9) .

文章引用: 吴磊 , 李召君 (2011) 关于不定方程(an-1)(bn-1)= X2解的研究。 理论数学, 1, 172-176. doi: 10.12677/pm.2011.13034

参考文献

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[2] L. Hajdu, L. Szalay. On the Diophantine equations and . Periodica Mathematica Hungarica, 2000, 40(2): 141-145.

[3] F. Luca, P. G. Walsh. The product of like-indexed terms in binary recurrences. Journal of Number Theory, 2002, 96(1): 152-173.

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[7] P. G. Walsh. On Diophantine equations of the form . Tatra Mountains Mathematical Publications, 2000, 20: 87-89.

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