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: the Pisano period π(n) is the smallest positive integer k such that F_{m+k} ≡ F_m (mod n) for all m | Statement: [Pisano period, property, the Pisano period π(n) is the smallest positive integer k such that F_{m+k} ≡ F_m (mod n) for all m]

Target entity: the Pisano period π(n) is the smallest positive integer k such that F_{m+k} ≡ F_m (mod n) for all m
Context triple: [Pisano period, property, the Pisano period π(n) is the smallest positive integer k such that F_{m+k} ≡ F_m (mod n) for all m]

• A. Pisano period chosen
  The Pisano period is the repeating cycle length of Fibonacci numbers when taken modulo a given integer.
• B. Fibonacci sequence
  The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
• C. 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.
• D. Lucas sequences
  Lucas sequences are a family of integer sequences defined by the same type of second-order linear recurrence as the Fibonacci numbers but with more general initial conditions, encompassing the Fibonacci sequence as a special case.
• 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.
• G. Unsure - the case is ambiguous/there is not enough information to decide.