Infinitely many positive solutions of the diophantine equation x2-kxy+y2+x=0

被引：4
|
作者：
Marlewski, A
Zarzycki, P
机构：
[1] Univ Gdansk, Dept Math, PL-80952 Gdansk, Poland
[2] Poznan Univ Tech, Inst Math, PL-60965 Poznan, Poland
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2004年 / 47卷 / 01期
关键词：
diophantine equations; computer algebra system; pell equation;
D O I：
10.1016/S0898-1221(04)90010-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the equation x(2) - kxy+y(2) + x = 0 with k is an element of N+ has an infinite number of positive integer solutions x and y if and only if k = 3. For k = 3 the quotient x/y is asymptotically equal to (3 + root5)/2 or (3 - root5)/2. Results of the paper are based on data obtained via Computer Algebra System (DERIVE 5). Some DERIVE procedures presented in the paper made it possible to discover interesting regularities concerning simple continued fractions of certain numbers. (C) 2004 Elsevier Ltd. All rights reserved.
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页码：115 / 121
页数：7
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