The method had been described earlier by Adrien-Marie Legendre in 1805, but Gauss claimed that he had been using it since 1795.

The method is based on the individual work of Carl Friedrich Gauss ( 1777 – 1855 ) and Adrien-Marie Legendre ( 1752 – 1833 ) combined with modern algorithms for multiplication and square roots.

* 1833 – Adrien-Marie Legendre, French mathematician ( b. 1752 )

The Legendre symbol was introduced by Adrien-Marie Legendre in 1798 in the course of his attempts at proving the law of quadratic reciprocity.

The early death of this talented mathematician, of whom Adrien-Marie Legendre said " quelle tête celle du jeune Norvégien!

Based on the tables by Anton Felkel and Jurij Vega, Adrien-Marie Legendre conjectured in 1797 or 1798 that π ( a ) is approximated by the function a /( A ln ( a ) + B ), where A and B are unspecified constants.

Germain first became interested in number theory in 1798 when Adrien-Marie Legendre published Essai sur la théorie des nombres.

* 1752 – Adrien-Marie Legendre, French mathematician ( d. 1833 )

* Adrien-Marie Legendre, French mathematician

* January 10 – Adrien-Marie Legendre, French mathematician ( b. 1752 )

* September 18 – Adrien-Marie Legendre, French mathematician ( d. 1833 )

The modern partial derivative notation is by Adrien-Marie Legendre ( 1786 ), though he later abandoned it ; Carl Gustav Jacob Jacobi re-introduced the symbol in 1841.

The idea of least-squares analysis was also independently formulated by the Frenchman Adrien-Marie Legendre in 1805 and the American Robert Adrain in 1808.

They are named after Adrien-Marie Legendre.

In April 1791, the academy's Metric Commission confided this mission to Jean-Dominique de Cassini, Adrien-Marie Legendre and Pierre Méchain.

# REDIRECT Adrien-Marie Legendre

Just prior to that time, Adrien-Marie Legendre had investigated the expansion of the Newtonian potential in powers of r = | x | and r < sub > 1 </ sub > = | x < sub > 1 </ sub >|.

Adrien-Marie Legendre, one of the referees, soon completed the proof for this case ; Dirichlet completed his own proof a short time after Legendre, and a few years later produced a full proof for the case.

* Adrien-Marie Legendre ( 1752 – 1833 ), a French mathematician

Adrien-Marie Legendre improved on the theorem in 1798 by stating that a positive integer can be expressed as the sum of three squares if and only if it is not of the form.

Classical orthogonal polynomials appeared in the early 19th century in the works of Adrien-Marie Legendre, who introduced the Legendre polynomials.

* Adrien-Marie Legendre gives the first published application of the method of least squares, in a supplement to his Nouvelles méthodes pour la détermination des orbites des cométes.

In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory.

* Johann Peter Gustav Lejeune Dirichlet and Adrien-Marie Legendre prove Fermat's last theorem for n = 5.

* Adrien-Marie Legendre publishes Éléments de géométrie, which becomes a popular textbook for many years.

Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between n < sup > 2 </ sup > and ( n + 1 )< sup > 2 </ sup > for every positive integer n. The conjecture is one of Landau's problems ( 1912 ) and remains unsolved.

The earliest form of regression was the method of least squares ( French: méthode des moindres carrés ), which was published by Legendre in 1805, and by Gauss in 1809.

It arose in part as a successor to the theory of Harmonic Grammar, developed in 1990 by Géraldine Legendre, Yoshiro Miyata and Paul Smolensky.

However after the election controversy developed as Legendre was not given a position on the Police Services Board.

Legendre was the first to publish the method, however.

The Legendre differential equation may be solved using the standard power series method.

Lagrange contributed extensively to the theory, and Legendre ( 1786 ) laid down a method, not entirely satisfactory, for the discrimination of maxima and minima.

Adrain, Gauss, and Legendre all motivated the method of least squares by the problem of reconciling disparate physical measurements ; in the case of Gauss and Legendre, the measurements in question were astronomical, and in Adrain's case they were survey measurements.

Legendre and Gauss both applied the method to the problem of determining, from astronomical observations, the orbits of bodies about the Sun ( mostly comets, but also later the then newly discovered minor planets ).

This is because given and, one can efficiently compute the Legendre symbol of, giving a successful method to distinguish from a random group element.

The central idea of the method is expressed by the following identity, sometimes called the Legendre identity:

It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude.

This makes the calculation using the Legendre symbol significantly slower than the one using the Jacobi symbol, as there is no known polynomial-time algorithm for factoring integers .< ref > The number field sieve, the fastest known algorithm, requires operations to factor N. See Cohen, p. 495 </ ref > In fact, this is why Jacobi introduced the symbol.

The term " Laplace's coefficients " was employed by William Whewell to describe the particular system of solutions introduced along these lines, whereas others reserved this designation for the zonal spherical harmonics that had properly been introduced by Laplace and Legendre.

In mathematics, Rodrigues's formula ( formerly called the Ivory – Jacobi formula ) is a formula for Legendre polynomials independently introduced by, and.

Legendre showed some of Germain's work in the Supplément to his second edition of the Théorie des Nombres, where he calls it très ingénieuse ( See Best Work on Fermat's Last Theorem ).