【摘要】 运用Pell方程和Jacobi符号的基本性质,给出Bremner定理的初等证明.即证明了丢番图方程3 X4-4Y4-2 X2+12Y2-9=0仅有正整数解(X,Y)=(1,1),(3,3).从而回答了柯召和孙琦在1983年提出的一个问题.更多还原

【Abstract】 By the recursion sequence of Pell equation and the properties of Jacobi symbol,we get an elementary proof of Bremner theorem.Namely the Diophantine equation 3X4-4Y4-2X2+12Y2-9=0 has only positive integer solutions(X,Y)=(1,1),(3,3).It is an answer to the open problem of KO Chao and SUN Qi in 1983.更多还原