This paper is concerned with the diophantine system, Ps1 i=1 xr i = Ps2 i=1 yr i , r = 1, 2, . . . , k, where s1 and s2 are integers such that the total number of terms on both sides, that is, s1+s2, is as small as possible. We define (k) to be the minimum value of s1+s2 for which there exists a nontrivial solution of this diophantine system. We show that (k) 2k for any arbitrary positive integer k. We also find several nontrivial solutions of the aforementioned diophantine system and thereby prove that (k) = 2k when k = 2, 3, 4 or 5.
展开▼
机译：本文涉及蒸番素系统，PS1 I = 1 XR I = PS2 I = 1 YR I，R = 1,2。 。 。 k，其中S1和S2是整数，使得两侧的总数，即S1 + S2尽可能小。我们将（k）定义为S1 + S2的最小值，其中该辅助系统的非竞争解决方案存在。我们向任何任意正整数k显示（k）2k。我们还发现了上述衍生体系的几种非增强溶液，从而证明（k）= 2k当k = 2,3,4或5时。
展开▼
