The two primes, p and q, should both be congruent to 3 (mod 4) (this guarantees that each quadratic residue has one square root which is also a quadratic residue) and gcd(φ(p-1), φ(q-1)) should be small (this makes the cycle length large).
The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be coprime to φ(N), and that 0 ≤ C < N.
Leonhard Euler | Euler | Green function | Graph of a function | Hash function | Schur function | Riemann zeta function | Euler characteristic | Dirac delta function | Bessel function | Euler Hermes | Monotonic function | Lateralization of brain function | function (mathematics) | Cryptographic hash function | Linear function | hash function | Gaussian function | function | Euler's totient function | Domain of unknown function | continuous function | Wave function | Quadratic function | Meijer G-function | Massieu function | Lyapunov function | Lambert W function | Gamma function | Function block diagram |
Euler used trial division, improving on Cataldi's method, so that at most 372 divisions were needed.
First implemented in METAFONT, AMS Euler was first used in the book Concrete Mathematics, co-authored by Knuth, which was dedicated to Euler.
Euler was born at Oelde in Westphalia and was educated at Oelde and at public schools in Cologne and Aachen and from 1885 started a career in engineering.
If spoke tension is increased beyond a safe level, the wheel spontaneously fails into a characteristic saddle shape (sometimes called a "taco" or a "pringle") like a three-dimensional Euler column.
In the letter, Euler talks of the problem of the Seven Bridges of Königsberg, a problem that Ehler brought to Euler’s attention.
Many famous mathematicians have studied such problems, including Euler, Legendre, and Gauss.
Goldbach is most noted for his correspondence with Leibniz, Euler, and Bernoulli, especially in his 1742 letter to Euler stating his Goldbach's conjecture.
Unlike computation of arbitrary integrals, however, Fourier-series integrations for periodic functions (like , by construction), up to the Nyquist frequency , are accurately computed by the equally spaced and equally weighted points for (except the endpoints are weighted by 1/2, to avoid double-counting, equivalent to the trapezoidal rule or the Euler–Maclaurin formula).
Independently from Euler and using the same methods, Maclaurin discovered the Euler–Maclaurin formula.
Actually this simple use of "quaternions" was first presented by Euler some seventy years earlier than Hamilton to solve the problem of magic squares.
The Neuberg cubic (named after Joseph Jean Baptiste Neuberg) is the locus of a point X such that X* is on the line EX, where E is the Euler infinity point (X(30) in the Encyclopedia of Triangle Centers).
For additional proofs, see Twenty Proofs of Euler's Formula by David Eppstein.
The Euler D.II was a German single-seat fighter, the successor to the earlier Euler D.I.
The Euler Society is an American group that is dedicated to the examination of the life and work of Leonhard Euler.
Bridges and buildings continued to be designed by precedent until the late 19th century, when the Eiffel Tower and Ferris wheel demonstrated the validity of the theory on large scales.
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but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century.
The field of mathematical demography was largely developed by Alfred J. Lotka in the early 20th century, building on the earlier work of Leonhard Euler.
Euler's problem also covers the case when the particle is acted upon by other inverse-square central forces, such as the electrostatic interaction described by Coulomb's law.
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Euler's three-body problem is to describe the motion of a particle under the influence of two centers that attract the particle with central forces that decrease with distance as an inverse-square law, such as Newtonian gravity or Coulomb's law.
According to Euler's theorem these 12 pentagons are required for closure of the carbon network consisting of n hexagons and C60 is the first stable fullerene because it is the smallest possible to obey this rule.
In the mid nineteenth century, the Gauss–Bonnet theorem linked the Euler characteristic to the Gaussian curvature.
Noam Elkies was first to find an infinite series of solutions to Euler's equation with exactly one variable equal to zero, thus disproving Euler's sum of powers conjecture for the fourth power.
Hessel also found Euler's formula disobeyed with interconnected polyhedra, for example, where an edge or vertex is shared by more than two faces (e.g. as in edge-sharing and vertex-sharing tetrahedra).
The Marquis de Condorcet's translation, made during the Age of Enlightenment, was notable for its omission of Euler’s theological references which Condorcet found as "anathema" to teaching science and rationalism.
In classical mechanics, Euler's three-body problem describes the motion of a particle in a plane under the influence of two fixed centers, each of which attract the particle with an inverse-square force such as Newtonian gravity or Coulomb's law.
Many famous mathematicians studied mathematical chess problems, for example, Euler, Legendre and Gauss.
Many mathematicians have studied differential equations and contributed to the field, including Newton, Leibniz, the Bernoulli family, Riccati, Clairaut, d'Alembert, and Euler.
In addition, he is Chairman of the Board of Domo, Nestlé Belgilux, and WDP, Vice-Chairman of the Board of Euler-Cobac and Member of the Board of Tractebel, Iris and Afinia Plastics.
This formula may be viewed as the 2-dimensional analogue of Euler's product formula for the number of integer partitions of n.
The Toolbox provides functions for manipulating and converting between datatypes such as: vectors;homogeneous transformations; roll-pitch-yaw and Euler angles and unit-quaternions which are necessary to represent 3-dimensional position and orientation.
Jameson, A. and Baker, T., "Solution of the Euler Equations for Complex Configurations", AIAA Paper, 83–1929 (1983).
Euler's assertion was not proved until the twentieth century, but almost a hundred years after his claim Joseph Liouville did manage to prove the existence of numbers that are not algebraic, something that until then had not been known for sure.
By assuming that plates are rigid and that the earth is spherical, Leonhard Euler’s theorem of motion on a sphere can be used to reduce the stability assessment to determining boundaries and relative motions of the interacting plates.