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’s formula for valuations of factorials | Statement: [Adrien-Marie Legendre, knownFor, Legendre’s formula for valuations of factorials]

Target entity: Legendre’s formula for valuations of factorials
Context triple: [Adrien-Marie Legendre, knownFor, Legendre’s formula for valuations of factorials]

• A. Hardy–Ramanujan asymptotic formula
  The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
• B. 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.
• C. Baker theorem on linear forms in logarithms
  The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
• D. Sylvester’s theorem on partitions
  Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
• E. Dirichlet hyperbola method
  The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
• 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: Legendre’s formula for valuations of factorials
Triple: [Adrien-Marie Legendre, knownFor, Legendre’s formula for valuations of factorials]

Legendre’s formula for valuations of factorials is a number-theoretic result that expresses the exponent of a prime in the prime factorization of n! as a sum of integer divisions of n by successive powers of that prime.

Target entity: Legendre’s formula for valuations of factorials
Target entity description: Legendre’s formula for valuations of factorials is a number-theoretic result that expresses the exponent of a prime in the prime factorization of n! as a sum of integer divisions of n by successive powers of that prime.

• A. Hardy–Ramanujan asymptotic formula
  The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
• B. 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.
• C. Baker theorem on linear forms in logarithms
  The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
• D. Sylvester’s theorem on partitions
  Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
• E. Dirichlet hyperbola method
  The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
• F. None of above. chosen