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: Euler criterion | Statement: [Legendre symbol, computableBy, Euler criterion]

Target entity: Euler criterion
Context triple: [Legendre symbol, computableBy, Euler criterion]

• A. Legendre symbol
  The Legendre symbol is a number-theoretic function that indicates whether an integer is a quadratic residue modulo an odd prime, taking values 1, −1, or 0 accordingly.
• B. Euler’s theorem
  Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
• C. Wilson's theorem
  Wilson's theorem is a result in number theory stating that a positive integer n > 1 is prime if and only if the factorial of (n − 1) is congruent to −1 modulo n.
• D. quadratic reciprocity law
  The quadratic reciprocity law is a fundamental theorem in number theory that characterizes when a quadratic equation modulo one odd prime has solutions in terms of solvability modulo another, revealing a deep symmetry between primes.
• E. Fermat's little theorem
  Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
• 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: Euler criterion
Triple: [Legendre symbol, computableBy, Euler criterion]

Euler criterion is a number-theoretic result that characterizes quadratic residues modulo an odd prime using exponentiation, providing a practical way to evaluate the Legendre symbol.

Target entity: Euler criterion
Target entity description: Euler criterion is a number-theoretic result that characterizes quadratic residues modulo an odd prime using exponentiation, providing a practical way to evaluate the Legendre symbol.

• A. Legendre symbol
  The Legendre symbol is a number-theoretic function that indicates whether an integer is a quadratic residue modulo an odd prime, taking values 1, −1, or 0 accordingly.
• B. Euler’s theorem
  Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
• C. Wilson's theorem
  Wilson's theorem is a result in number theory stating that a positive integer n > 1 is prime if and only if the factorial of (n − 1) is congruent to −1 modulo n.
• D. quadratic reciprocity law
  The quadratic reciprocity law is a fundamental theorem in number theory that characterizes when a quadratic equation modulo one odd prime has solutions in terms of solvability modulo another, revealing a deep symmetry between primes.
• E. Fermat's little theorem
  Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
• F. None of above. chosen

Target predicate: computableBy
Context triple: [Legendre symbol, computableBy, Euler criterion]

• A. computationalClass
  Indicates that two entities share the same computational complexity class or that one entity is categorized within a specified computational complexity class.
• B. usesComputationMethod chosen
  Indicates that an entity performs its processing or decision-making by applying a specified computational method or algorithm.
• C. isUsedToCompute
  Indicates that one entity serves as an input, basis, or resource for performing a calculation or deriving a result about another entity.
• D. turingComplete
  Indicates that a system or language is capable of performing any computation that a universal Turing machine can, given enough time and memory.
• E. computes
  Indicates that one entity performs a calculation or processing operation to produce a result from given data or inputs.
• F. None of above.