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The quadratic character of 1+\sqrt{2} and an elliptic curve

Yu Tsumura

Published 2010-01-03Version 1

When p is congruent to 1 mod 8, we have a criterion of the quadratic character of 1+\sqrt{2}, which is related to the class number of \Q(\sqrt{-p}). In this paper, we obtain a similar criterion using an elliptic curve, which contrasts to the proof using algebraic number theory for the old one.

Comments: 4 pages
Categories: math.NT
Subjects: 11G20, 11E25
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