不定方程 x3＋y3＝z3＋w3的一种解法

摘要

Linear substitution is performed on four variable cubic equation x3 +y3 =z3 +w3 , which is trans-formed into au2 =bv2 +b3 -a33 .Given a and b, a two variable quadratic equation and an initial solution U( u0 ,v0 ) are obtained , and thus to find the transformation matrix A .By repeatedly applying the transformation matrix to the initial solution U, and inverse substitution , infinitely many integer solutions of the four variable cubic equation can be obtained .%对于四元三次不定方程x3＋y3＝z3＋w3，实施线性变量代换，将方程变为au2＝bv2＋b3－a33，给定a，b，使其变为二元二次不定方程，找到一个初始解U（ u0，v0），从而找到解变换矩阵A，变换矩阵反复作用于初始解U，再进行逆代换，从而得到四元三次方程的无穷多整数解。