A combinatorial proof of the quadratic Gauss sum

Abstract

We provide an elementary approach to computing the quadratic Gauss sum, emphasizing the method employed to compute the sum corresponding to multiples of 4. The proof method employed does not rely on the law of quadratic reciprocity, but only on exploiting symmetries among the sum's components, together with a recursive approach.

arXiv comment9 pages. No AI was used for this paper