Octic reciprocity
id:
octic-reciprocity-264-7638643
title:
Octic reciprocity
text:
In number theory, octic reciprocity is a reciprocity law relating the residues of 8th powers modulo primes, analogous to the law of quadratic reciprocity, cubic reciprocity, and quartic reciprocity. There is a rational reciprocity law for 8th powers, due to Williams. Define the symbol 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 8, such that 4 = 4 = + 1. Let p = a2 + b2 = c2 + 2d2 and q = A2 + B2 = C2 + 2D2, with aA odd
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wiki
category slug:
encyclopedia
description:
Reciprocity law relating the residues of 8th powers modulo primes
original url:
https://en.wikipedia.org/wiki/Octic_reciprocity
date created:
date modified:
2022-08-21T22:23:12Z
main entity:
{"identifier":"Q7076857","url":"https://www.wikidata.org/entity/Q7076857"}
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13
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