ON THE SYSTEM OF DIOPHANTINE EQUATIONS x~2 - 6y~2 = - 5 and x = 2z~2 - 1

摘要

Our system of equations is a quartic model of an elleptic curve. It has only finitely many integer solutions by a well known result of Siegel [11], moreover they are effectively computable by Baker [1], It is still interesting to solve it, because the elementary method of J. H. E. Cohn [3], which was further develop-ed by McDaniel and Ribenboim [4] failed. The Siegel-Baker method, which is the combination of algebraic and transcendental number theoretical tools is complicated. It requires detailed knowledge of certain quartic number fields and the solution of several quartic Thue equations.