second supplementary law
E662762
The second supplementary law is a classical result in number theory that specifies the behavior of the Legendre symbol for the prime 2, complementing the quadratic reciprocity law.
All labels observed (1)
| Label | Occurrences |
|---|---|
| second supplementary law canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7420202 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: second supplementary law Context triple: [quadratic reciprocity law, hasSupplement, second supplementary law]
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A.
Second Home Rule Bill
The Second Home Rule Bill was an 1893 legislative proposal by British Prime Minister William Gladstone to grant Ireland limited self-government within the United Kingdom, a key milestone in the Irish struggle for autonomy despite ultimately being rejected by the House of Lords.
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B.
Complementary Law 179 of 2021
Complementary Law 179 of 2021 is the Brazilian statute that granted formal operational autonomy and fixed-term mandates to the Central Bank of Brazil’s leadership, insulating monetary policy from short-term political influence.
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C.
Simpson–Mazzoli Act
The Simpson–Mazzoli Act is a landmark 1986 U.S. federal law that overhauled immigration policy by granting amnesty to certain undocumented immigrants while imposing new sanctions on employers who hired unauthorized workers.
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D.
Basic Law V
Basic Law V is a central axiom in Frege’s logical system that equates the extensions of concepts with identical truth conditions, and whose inconsistency famously undermined his logicist foundation for arithmetic.
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E.
Nunuku’s Law
Nunuku’s Law is a foundational Moriori pacifist code that forbids warfare and violence, shaping the community’s identity and social conduct.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: second supplementary law Target entity description: The second supplementary law is a classical result in number theory that specifies the behavior of the Legendre symbol for the prime 2, complementing the quadratic reciprocity law.
-
A.
Second Home Rule Bill
The Second Home Rule Bill was an 1893 legislative proposal by British Prime Minister William Gladstone to grant Ireland limited self-government within the United Kingdom, a key milestone in the Irish struggle for autonomy despite ultimately being rejected by the House of Lords.
-
B.
Complementary Law 179 of 2021
Complementary Law 179 of 2021 is the Brazilian statute that granted formal operational autonomy and fixed-term mandates to the Central Bank of Brazil’s leadership, insulating monetary policy from short-term political influence.
-
C.
Simpson–Mazzoli Act
The Simpson–Mazzoli Act is a landmark 1986 U.S. federal law that overhauled immigration policy by granting amnesty to certain undocumented immigrants while imposing new sanctions on employers who hired unauthorized workers.
-
D.
Basic Law V
Basic Law V is a central axiom in Frege’s logical system that equates the extensions of concepts with identical truth conditions, and whose inconsistency famously undermined his logicist foundation for arithmetic.
-
E.
Nunuku’s Law
Nunuku’s Law is a foundational Moriori pacifist code that forbids warfare and violence, shaping the community’s identity and social conduct.
- F. None of above. chosen
Statements (29)
| Predicate | Object |
|---|---|
| instanceOf |
result in quadratic reciprocity
ⓘ
theorem in number theory ⓘ |
| appliesTo | odd prime p ⓘ |
| assumes | p is an odd prime ⓘ |
| characterizes | quadratic character of 2 modulo an odd prime ⓘ |
| complements | quadratic reciprocity law ⓘ |
| concerns | quadratic residues modulo odd primes ⓘ |
| dependsOn |
definition of Legendre symbol
ⓘ
properties of quadratic residues modulo primes ⓘ |
| field | number theory ⓘ |
| hasAlternativeFormulation | (2/p) = (-1)^{(p^2-1)/8} for odd prime p ⓘ |
| hasAlternativeName | second supplementary law to quadratic reciprocity ⓘ |
| holdsIn | ring of integers modulo p ⓘ |
| implies |
2 is a quadratic nonresidue modulo p if and only if p ≡ 3 or 5 (mod 8)
ⓘ
2 is a quadratic residue modulo p if and only if p ≡ 1 or 7 (mod 8) ⓘ |
| involves | prime number 2 ⓘ |
| isPartOf | supplementary laws to quadratic reciprocity ⓘ |
| isSupplementaryTo |
first supplementary law
ⓘ
third supplementary law ⓘ |
| isUsedIn |
computing Legendre symbols
ⓘ
elementary proofs in quadratic reciprocity ⓘ primality testing arguments ⓘ study of quadratic fields ⓘ |
| relatedTo |
Legendre symbol
ⓘ
quadratic reciprocity law ⓘ |
| specifies | behavior of the Legendre symbol for the prime 2 ⓘ |
| states |
for an odd prime p, (2/p) = -1 if p ≡ ±3 (mod 8)
ⓘ
for an odd prime p, (2/p) = 1 if p ≡ ±1 (mod 8) ⓘ |
| uses |
Legendre symbol (2/p)
ⓘ
linked to:
Legendre symbol
|
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: second supplementary law Description of subject: The second supplementary law is a classical result in number theory that specifies the behavior of the Legendre symbol for the prime 2, complementing the quadratic reciprocity law.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.