Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Gauss’s Eureka theorem on triangular numbers | Statement: [Fermat polygonal number theorem, generalizes, Gauss’s Eureka theorem on triangular numbers]

Target entity: Gauss’s Eureka theorem on triangular numbers
Context triple: [Fermat polygonal number theorem, generalizes, Gauss’s Eureka theorem on triangular numbers]

• A. Gauss’s remarkable theorem
  Gauss’s remarkable theorem is a fundamental result in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
• 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. 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.
• D. Gauss’s lemma in number theory
  Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
• E. Three Pearls of Number Theory
  Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Gauss’s Eureka theorem on triangular numbers
Triple: [Fermat polygonal number theorem, generalizes, Gauss’s Eureka theorem on triangular numbers]

Gauss’s Eureka theorem on triangular numbers is a result in number theory stating that every positive integer can be expressed as a sum of three triangular numbers.

Target entity: Gauss’s Eureka theorem on triangular numbers
Target entity description: Gauss’s Eureka theorem on triangular numbers is a result in number theory stating that every positive integer can be expressed as a sum of three triangular numbers.

• A. Gauss’s remarkable theorem
  Gauss’s remarkable theorem is a fundamental result in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
• B. Fermat polygonal number theorem chosen
  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. 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.
• D. Gauss’s lemma in number theory
  Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
• E. Three Pearls of Number Theory
  Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
• F. None of above.