广义Pell方程Ax2-By2=4的通解公式

摘要

The main purpose of this paper is using the parity of Lucas numbers, to discuss the integer solutions (x, y) of the equation when A, B be positive integers such that A > 1, 2 - AB, and AB is not a complete square, which gives a general solution formula of integer solutions (x, y) of the equation Ax2-By2 = 4 with gcd(x, y)=1.%主要运用 Lucas 数的奇偶性,讨论了当 A, B 是适合 A>1,2-AB 且 AB 非平方数的正整数时,广义 Pell 方程的整数解(x, y),即给出了方程 Ax2By2=4适合gcd(x, y)=1的整数解(x, y)的通解公式。