|
This article is cited in 2 scientific papers (total in 2 papers)
An elementary algorithm for solving a diophantine equation of degree four with Runge's condition
Nikolai N. Osipov, Maria I. Medvedeva Institute of Space and Information Technology, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
Abstract:
We propose an elementary algorithm for solving a diophantine equation
\begin{equation*}
(p(x,y)+a_1x+b_1y)(p(x,y)+a_2x+b_2y)-dp(x,y)-a_3x-b_3y-c=0 \tag{*}
\end{equation*}
of degree four, where $p(x,y)$ denotes an irreducible quadratic form of positive discriminant and $(a_1,b_1) \neq (a_2,b_2)$. The last condition guarantees that the equation $(*)$ can be solved using the well known Runge's method, but we prefer to avoid the use of any power series that leads to upper bounds for solutions useless for a computer implementation.
Keywords:
diophantine equations, elementary version of Runge's method.
Received: 16.08.2018 Received in revised form: 18.10.2018 Accepted: 01.04.2019
Citation:
Nikolai N. Osipov, Maria I. Medvedeva, “An elementary algorithm for solving a diophantine equation of degree four with Runge's condition”, J. Sib. Fed. Univ. Math. Phys., 12:3 (2019), 331–341
Linking options:
https://www.mathnet.ru/eng/jsfu765 https://www.mathnet.ru/eng/jsfu/v12/i3/p331
|
Statistics & downloads: |
Abstract page: | 243 | Full-text PDF : | 115 | References: | 23 |
|