An Elementary Algorithm for Solving a Diophantine Equation of Degree Four with Runge's Condition
Скачать файл:
URI (для ссылок/цитирований):
http://journal.sfu-kras.ru/en/article/110245https://elib.sfu-kras.ru/handle/2311/128926
Автор:
Osipov, N. N.
Medvedeva, M. I.
Коллективный автор:
Институт космических и информационных технологий
Кафедра прикладной математики и компьютерной безопасности
Дата:
2019Журнал:
Journal of Siberian Federal University - Mathematics and PhysicsКвартиль журнала в Scopus:
Q3Квартиль журнала в Web of Science:
без квартиляБиблиографическое описание:
Osipov, N. N. An Elementary Algorithm for Solving a Diophantine Equation of Degree Four with Runge's Condition [Текст] / N. N. Osipov, M. I. Medvedeva // Journal of Siberian Federal University - Mathematics and Physics. — 2019. — Т. 12 (№ 3). — С. 331-341Аннотация:
We propose an elementary algorithm for solving a diophantine equation (p(x, y) + a1x + b1y)(p(x, y) + a2x + b2y)-dp(x, y)-a3x-b3y-c = 0 (*) of degree four, where p(x, y) denotes an irreducible quadratic form of positive discriminant and (a1; b1) ̸= (a2; b2). 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.