Biquadratic Reciprocity Laws
نویسندگان
چکیده
منابع مشابه
Biquadratic reciprocity and a Lucasian primality test
Let {sk, k ≥ 0} be the sequence defined from a given initial value, the seed, s0, by the recurrence sk+1 = s 2 k − 2, k ≥ 0. Then, for a suitable seed s0, the number Mh,n = h · 2n − 1 (where h < 2n is odd) is prime iff sn−2 ≡ 0 mod Mh,n. In general s0 depends both on h and on n. We describe a slight modification of this test which determines primality of numbers h·2n±1 with a seed which depends...
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The purpose of this note is to provide an overview of Rational Reciprocity (and in particular, of Scholz’s reciprocity law) for the non-number theorist. In the first part, we will describe the background in number theory that will be necessary for a complete understanding of the material to be discussed in the second part. The second part focuses on a proof of Scholz’s reciprocity law using the...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.2307/2039442