Legendre symbol

English Etymology Named after French mathematician Adrien-Marie Legendre (1752–1833), who introduced the symbol in 1798 in his work Essai sur la Théorie des Nombres ("Essay on the Theory of Numbers"). Noun en number theory A mathematical function of an integer and a prime number, written , which indicates whether a is a quadratic residue modulo p. 1994, James K. Strayer, Elementary Number Theory, Waveland Press, 2002, Reissue, page 109, Our only method at present for the computation of Legendre symbols requires a possible consideration of congruences (unless, of course, we are fortunate enough to encounter the desired quadratic residue along the way). en 2006 Neville Robbins Beginning Number Theory Jones & Bartlett 2nd https://books.google.com.au/books?id=TtLMrKDsDuIC&pg=PA195&dq=%22Legendre+symbol%22%7C%22Legendre+symbols%22&hl=en&sa=X&ved=0ahUKEwiY7p694urWAhUHf7wKHelECP4Q6AEIUjAI#v=onepage&q=%22Legendre%20symbol%22%7C%22Legendre%20symbols%22&f=false 195 The Jacobi symbol, which generalizes the Legendre symbol, sheds some additional light on how to determine whether (7.29) has solutions when m has two or more distinct prime factors. en 2013 Song Y. Yan Number Theory for Computing https://books.google.com.au/books?id=KAqrCAAAQBAJ&pg=PA149&dq=%22Legendre+symbol%22%7C%22Legendre+symbols%22&hl=en&sa=X&ved=0ahUKEwiY7p694urWAhUHf7wKHelECP4Q6AEIajAM#v=onepage&q=%22Legendre%20symbol%22%7C%22Legendre%20symbols%22&f=false 149 Springer Jacobi symbols can be used to facilitate the calculation of Legendre symbols. In fact, Legendre symbols can be eventually calculated by Jacobi symbols [17]. That is, the Legendre symbol can be calculated as if it were a Jacobi symbol. For example, consider the Legendre symbol where 335 = 5·67 is not a prime (of course, 2999 is a prime, otherwise, it is not a Legendre symbol). Usage notes The symbol takes the values: It is generalised to composite numbers by the Jacobi symbol, which is identical in form and range of values and is defined as a product of Legendre symbols. See also en Euler's criterion en Jacobi symbol en quadratic reciprocity en eponyms