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: Prouhet–Tarry–Escott problem | Statement: [Erdős–Moser equation, isRelatedTo, Prouhet–Tarry–Escott problem]

Target entity: Prouhet–Tarry–Escott problem
Context triple: [Erdős–Moser equation, isRelatedTo, Prouhet–Tarry–Escott problem]

• A. Erdős–Moser equation
  The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
• B. Waring's problem
  Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
• C. 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.
• D. Pillai’s conjecture
  Pillai’s conjecture is an unproven statement in number theory asserting that the difference between perfect powers takes each positive integer value only finitely many times.
• E. Ramanujan–Nagell equation
  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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Prouhet–Tarry–Escott problem
Target entity description: The Prouhet–Tarry–Escott problem is a classic number theory problem that asks for distinct integer multisets whose powers up to a given degree have equal sums, making it a central example in the study of equal-sum power partitions and Diophantine equations.

• A. Erdős–Moser equation
  The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
• B. Waring's problem
  Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
• C. 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.
• D. Pillai’s conjecture
  Pillai’s conjecture is an unproven statement in number theory asserting that the difference between perfect powers takes each positive integer value only finitely many times.
• E. Ramanujan–Nagell equation
  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.
• F. None of above. chosen