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: Legendre symbol takes values ±1 for a coprime to p | Statement: [Gauss’s lemma (number theory), implies, Legendre symbol takes values ±1 for a coprime to p]

Target entity: Legendre symbol takes values ±1 for a coprime to p
Context triple: [Gauss’s lemma (number theory), implies, Legendre symbol takes values ±1 for a coprime to p]

• A. Gauss’s lemma in number theory chosen
  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.
• B. 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.
• 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. Gaussian periods
  Gaussian periods are special algebraic sums of roots of unity that play a key role in number theory, particularly in constructing regular polygons like the 17-gon with straightedge and compass and in understanding cyclotomic fields.
• E. Euler’s totient function φ(n)
  Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.