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: Diophantine equations decision problem | Statement: [Hilbert problems, notableProblem, Diophantine equations decision problem]

Target entity: Diophantine equations decision problem
Context triple: [Hilbert problems, notableProblem, Diophantine equations decision problem]

• A. Hilbert’s tenth problem chosen
  Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
• B. Entscheidungsproblem
  The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
• 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. 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.
• E. Hilbert’s Nullstellensatz
  Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.