Rational reciprocity law
id:
rational-reciprocity-law-198-1552976
title:
Rational reciprocity law
text:
In number theory, a rational reciprocity law is a reciprocity law involving residue symbols that are related by a factor of +1 or –1 rather than a general root of unity. As an example, there are rational biquadratic and octic reciprocity laws. Define the symbol (x|p)k to be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 4, such that (p|q)2 = (q|p)2 = +1. Let p = a2 + b2 and q = A2 + B2 with aA odd. Then If in addition p and q are
brand slug:
wiki
category slug:
encyclopedia
description:
Number theory concept
original url:
https://en.wikipedia.org/wiki/Rational_reciprocity_law
date created:
date modified:
2021-10-02T20:55:04Z
main entity:
{"identifier":"Q7295777","url":"https://www.wikidata.org/entity/Q7295777"}
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fields total:
13
integrity:
14