Rational Cube And Additive Number Theory, A Number Of Issues

In this dissertation, we investigate rational cuboids and some problems in additive number theory. The main results are summarized as follows.1. A rational cuboid is a rectangular parallelepiped whose edges and face diagonals all have rational lengths. The problem of finding rational cuboids has attracted much historical interest. Are there rational cuboids with a given face? We pose this problem and develop a general theory to deal with this problem. In a sense, we reduce this problem to a finite calculation.