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 is only defined for odd prime moduli | Statement: [Jacobi symbol, differenceFrom, Legendre symbol is only defined for odd prime moduli]

Target entity: Legendre symbol is only defined for odd prime moduli
Context triple: [Jacobi symbol, differenceFrom, Legendre symbol is only defined for odd prime moduli]

• A. Legendre symbol chosen
  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 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.
• C. 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.
• D. Jacobi symbol
  The Jacobi symbol is a number-theoretic function that generalizes the Legendre symbol and plays a key role in quadratic residues and primality testing in modular arithmetic.
• E. Gauss’s lemma in number theory
  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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.