A NEW SOLUTION OF THE DIOPHANTINE EQUATION X(2)+1=2Y(4)

[摘要] In this paper we use the method of Thue and Siegel, based on explicit Pade approximations to algebraic functions, to solve the equation given in the title. We present an upper bound for the solutions of the Thue equation X4-12X2Y2 + 16XY3-4Y4 = N, namely \y\ < 4.233 x 10(7) X \N\ 1/0.676 . For \N\ = 1 we use this bound to solve the equation X2 + 1 = 2y4. (C) 1994 Academic Press, Inc.

[发布日期] 1994-07-01