 About 7,330 results  books.google.com Several very important factorization methods, old as well as modem, make use of
Legendre's congruence. They differ only in the way in which a solution to x2 E ya
mod N is found. As examples, we can mention the method of Fermat already ... 

 books.google.com Legendre's Constant Legendre's Formula 1737 Lewin, L. "Legendre's Chi
Function. ... POLYNOMIAL, MACLAURIN SERIES, Pico NE'S THEOREM,
TAYLOR SERIES Legendre's Factorization Method A PRIME FACTORIZATION
ALGORITHM ... 

 books.google.com 4.2.3. Legendre's. Congruence. In the next two subsections, we shall introduce
three widely used general purpose integer factorization methods, namely, the
continued fraction method (abbreviated CFRAC), the quadratic sieve (
abbreviated ... 

 books.google.com Mathematical Methods in Science and Engineering's modular structure affords instructors enough flexibility to use this book for several different advanced undergraduate and graduate level courses. 

 books.google.com Legendre's method Legendre (1752–1833) considered a related idea. ... and
searched for solutions of the congruence, x2 p (mod N) Carl Pomerance Recalls “
When I give talks on factoring, I often repeat an incident that happened to me
long ... 

 books.google.com EXAMPLE 1: Find the eigenvalues and eigenfunctions of the associated
Legendre differential equation by use of the factorization method. Solution: By
use of the transformation u = P sin1/2 θ, the associated Legendre differential
equation [the ... 

 books.google.com ... function for Bessel functions of the first kind of integer order 159 generating
function for Legendre polynomials 1512 ... LU factorization method 149 lu(A)
MATLAB function 1412, 1414 M Maclaurin power series 641, 76 main
diagonal ... 

 books.google.com Jacobi symbols can be used to facilitate the calculation of Legendre symbols. In
fact, Legendre symbols can be eventually calculated by Jacobi symbols. That is,
the Legendre symbol can be calculated as if it were ( 335 2999 ) , a Jacobi ... 

 books.google.com ... PierreSimon, 476 LDLt factorization, 268 Least squares continuous, 329, 350
discrete, 321 general, 325 linear, 324 Leastchange secant update method, 421
Legendre polynomial, 134, 335 Legendre, AdrienMarie, 135 Leibniz, Gottfried, ... 

 books.google.com Like the original PL method, we seek a nonzero solution q∗ such that the
magnitude of Apaq∗ is minimized over all possible q of unit length. Again, we
use Singular Value Decomposition method to solve this minimization problem.
Once q∗ ... 

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