Ramanujan–Nagell equation
E355435
The Ramanujan–Nagell equation is a famous Diophantine equation in number theory that has only finitely many integer solutions and is closely associated with the work of Srinivasa Ramanujan.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Ramanujan–Nagell equation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3410518 — 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: Ramanujan–Nagell equation Context triple: [Srinivasa Ramanujan, notableWork, Ramanujan–Nagell equation]
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A.
Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
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B.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
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C.
Lagrange's four-square theorem
Lagrange's four-square theorem is a fundamental result in number theory stating that every natural number can be expressed as the sum of four integer squares.
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D.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
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E.
Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
- 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: Ramanujan–Nagell equation Target entity description: The Ramanujan–Nagell equation is a famous Diophantine equation in number theory that has only finitely many integer solutions and is closely associated with the work of Srinivasa Ramanujan.
-
A.
Fermat's theorem on sums of two squares
Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
-
B.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
-
C.
Lagrange's four-square theorem
Lagrange's four-square theorem is a fundamental result in number theory stating that every natural number can be expressed as the sum of four integer squares.
-
D.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
E.
Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
Diophantine equation
ⓘ
exponential Diophantine equation ⓘ |
| appearsIn | the study of perfect powers near squares ⓘ |
| baseOfExponentialTerm | 2 ⓘ |
| canBeViewedAs | elliptic curve over the rationals ⓘ |
| classification |
Thue-type equation
ⓘ
linked to:
Diophantine equations
|
| coefficientOfConstantTerm | 7 ⓘ |
| curveType | hyperelliptic curve ⓘ |
| degreeIn2 | n ⓘ |
| degreeInX | 2 ⓘ |
| difficulty | historically difficult to solve completely ⓘ |
| domainOfVariables | integers ⓘ |
| exponentVariable | n ⓘ |
| field | number theory ⓘ |
| genus | 1 ⓘ |
| hasFiniteNumberOfSolutions | true ⓘ |
| hasForm | x^2 + 7 = 2^n ⓘ |
| hasGeneralization | equations of the form x^2 + D = k^n ⓘ |
| isFamousFor |
being conjectured by Srinivasa Ramanujan
ⓘ
having exactly five integer solutions ⓘ |
| namedAfter |
Srinivasa Ramanujan
ⓘ
Trygve Nagell ⓘ |
| numberOfIntegerSolutions | 5 ⓘ |
| property | has only finitely many integer solutions ⓘ |
| quadraticVariable | x ⓘ |
| relatedTo |
Lebesgue–Nagell equation
ⓘ
Mordell equation ⓘ
linked to:
Mordell curve
Pillai’s conjecture ⓘ |
| solution |
(x,n) = (1,3)
ⓘ
(x,n) = (11,7) ⓘ (x,n) = (181,15) ⓘ (x,n) = (3,4) ⓘ (x,n) = (5,5) ⓘ |
| solutionType | integer solutions only ⓘ |
| status | completely solved ⓘ |
| topic |
exponential Diophantine problems
ⓘ
integer points on curves ⓘ |
| usedAsExampleIn |
expositions on elliptic curves
ⓘ
surveys on exponential Diophantine equations ⓘ texts on Diophantine equations ⓘ |
| variable |
n
ⓘ
x ⓘ |
| wasProvedBy | Trygve Nagell ⓘ |
| yearOfCompleteProof | 1948 ⓘ |
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: Ramanujan–Nagell equation Description of subject: The Ramanujan–Nagell equation is a famous Diophantine equation in number theory that has only finitely many integer solutions and is closely associated with the work of Srinivasa Ramanujan.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.