논문KCI 등재
On the additive structure of the set of quadratic residues modulo p
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Abstract
It is well-known that the set of quadratic residues modulo p forms multiplicative group. But except for very special cases, there is no result on the sum of quadratic residues or non-residues. Here we study three different sums; the sum of two quadratic residues, the sum of two quadratic non-residues and the sum of a quadratic residue with a non-residue. Bachet elliptic curves are the curves of the form y2 = x3 + a3 where a is a fixed element of the underlying field. Studying the rational points on these curves depends on our knowledge of the sum of a variable x3 and a fixed value a. Therefore we study such sums as well.
참고문헌 (11)
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