Equal Sums of Like Powers with Minimum Number of Terms

Abstract: This paper is concerned with the diophantine system,

s u m_{i = 1}^{s_{1}} x_{i}^{r} = s u m_{i = 1}^{s_{2}} y_{i}^{r},, r = 1,, 2,, l d o t s,, k,

where

s_{1}

and

s_{2}

are integers such that the total number of terms on both sides, that is,

s_{1} + s_{2},

is as small as possible. We define

to be the minimum value of

s_{1} + s_{2}

for which there exists a nontrivial solution of this diophantine system. We find nontrivial integer solutions of this diophantine system when

k < 6

, and thereby show that

and

.

Full work available at URL: https://arxiv.org/abs/1602.08698

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