On the quadratic character of quadratic units
نویسندگان
چکیده
منابع مشابه
On the Quadratic Character of Quadratic Units
Let p ≡ 1 (mod 4) be a prime. Let a, b ∈ Z with p a(a2 + b2). In the paper we mainly determine ( b+ √ a2+b2 2 ) p−1 2 (mod p) by assuming p = c2 + d2 or p = Ax2 + 2Bxy + Cy2 with AC − B2 = a2 + b2. As an application we obtain simple criteria for εD to be a quadratic residue (mod p), where D > 1 is a squarefree integer such that D is a quadratic residue of p, εD is the fundamental unit of the qu...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2008
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2007.07.009