ON THE HOMOGENEOUS CONE 3x~2 - 8y~2 = 25z~2

摘要

This paper aims at determining non-zero distinct integer solutions satisfying the homogeneous cone represented by the ternary quadratic equation 3x~2 - 8y~2 = 25z~2. A few interesting relations among the solutions are presented. A general formula for generating sequence of integer solutions to the given cone based on a given solution is illustrated.