2 мая 2016 г. · The purpose of this article is to show how to solve the Diophantine Equation Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0.

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, where a, c, and k are specified (positive or negative) integers.

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques ...

The quadratic diophantine equations are equations of the type: where a, b, c and d are integers, and we ask the solutions x and y to be integers.

23 сент. 2013 г. · If we set X=2x+1, Y=2y+1 and Z=2z+1, we get the equation X2+1=Y2+Z2. Euler showed that all solutions have the form (ac+bd)2+1=(ac−bd)2+(ad+bc)2 ... On quadratic Diophantine equations with n variables Solutions of a quadratic Diophantine equation over algebraic ... Другие результаты с сайта mathoverflow.net

In proving Theorems 2 and 3, we use the Pell equation in quadratic fields, (3) e - yv2 = 1. In this connection, we prove the following theorem.

9 сент. 2023 г. · Solving the quadratic diophantine equation ax + bxy + cy + dx + ey + f = 0 (general case).

25 нояб. 2013 г. · If f(x,y), and f(x0,y0)=0, then the polynomial ft(s)=f(x+s,y+st) is a quadratic polynomial in one variable, which has a zero at s=0. Alternative method to solve quadratic Diophantine equations Quadratic Diophantine equations in two variables Другие результаты с сайта math.stackexchange.com

In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, for which only ...

Продолжительность: 11:04
Опубликовано: 26 дек. 2020 г.