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: Fermat numbers | Statement: [Fermat number, hasSequenceName, Fermat numbers]

Target entity: Fermat numbers
Context triple: [Fermat number, hasSequenceName, Fermat numbers]

• A. Fermat number chosen
  A Fermat number is a special type of integer of the form \(F_n = 2^{2^n} + 1\), studied in number theory for its intriguing properties related to primality and constructible polygons.
• 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. Bernoulli numbers
  Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
• E. Lucas sequences
  Lucas sequences are a family of integer sequences defined by the same type of second-order linear recurrence as the Fibonacci numbers but with more general initial conditions, encompassing the Fibonacci sequence as a special case.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasSequenceName
Context triple: [Fermat number, hasSequenceName, Fermat numbers]

• A. hasCollectionNamedAfter
  Indicates that an entity has a collection (e.g., of works, items, or artifacts) that is named in honor of or after another entity.
• B. hasGenericName
  Indicates that an entity is associated with a non-brand, generic name that designates its general type or class.
• C. hasSuccessorNameConflict
  Indicates that an entity’s successor has a name that conflicts (e.g., duplicates or clashes) with another existing or expected name in the system.
• D. hasGivenNameUsage
  Indicates that an entity is associated with a particular way or context in which its given name is used.
• E. hasComponentName
  Indicates that an entity includes or is associated with a component identified by a specific name.
• F. None of above. chosen