Euler's conjecture, a theory proposed by Leonhard Euler in 1769, hung in there for 200 years. Then L.J. Lander and T.R. Parkin came along in 1966, and debunked the conjecture in two swift sentences. Their article -- which is now open access and can be downloaded here -- appeared in the *Bulletin of the American Mathematical Society*. If you're wondering what the conjecture and its refutation are all about, you might want to ask Cliff Pickover, the author of 45 books on math and science. He brought this curious document to the web last week.

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This article is even shorter: On a conjecture of R. J. Simpson about exact covering congruences

Author: Doron Zeilberger Drexel Univ., Philadelphia, PA

Published in: American Mathematical Monthly archive

Volume 96 Issue 3, March 1989 Page 243

http://www.jstor.org/discover/10.2307/2325213?uid=3739864&uid=2134&uid=2&uid=70&uid=4&uid=3739256&sid=21106466966333

Here is a longer version of the same article:

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/simpson.pdf

My contribution to this topic:

Short post, short papers, enjoy! LOG#170. The shortest papers ever: the list.

http://www.thespectrumofriemannium.com/2015/04/13/log170-the-shortest-papers-ever-the-list/

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MATHEMATICS AND EDUCATION

ABSTRACT

]. In these approaches one may derive covariant versions of the Fokker-Planck equation of Brownian motion in curved spaces. The mathematical approach to path integrals uses similar techniques [5]. The inherent ambiguities can be removed by demanding a certain form for Schrödinger equation of the system, which in curved space is have the Laplace-Beltrami operator as an operator for the kinetic energy [2], without an additional curvature scalar.

also here we can development some aspects as say prof dr mircea orasanu and prof horia orasanu

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GAUSS AND EULER

ABSTRACT

Let’s approach Leonhard Euler and his work the same way. It will make things a whole lot easier.

If one is not a mathematician (and except for a few of you out there, who is?), it’s going to be impossible to actually understand why Euler was such a great man. Other people will have to tell us, and we should probably believe them.

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PROBLEM OF OPEN CULTURE AND APPLICATIONS

ABSTRACT

In general, partial differential equations are difficult to solve, but techniques have been developed for simpler classes of equations called linear, and for classes known loosely as “almost” linear, in which all derivatives of an order higher than one occur to the first power and their coefficients involve only the independent variables.

Many physically important partial differential equations are second-order and linear. For example:

uxx + uyy = 0 (two-dimensional Laplace equation)

uxx = ut (one-dimensional heat equation)

uxx − uyy = 0 (one-dimensional wave equation)

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PFAFF FORMS AND CONSEQUENCES

ABSTRACT

If is an even integer, the series reduces to a polynomial of degree with only even powers of and the series diverges. If is an odd integer, the series reduces to a polynomial of degree with only odd powers of and the series diverges. The general solution for an integer is then given by the Legendre polynomials

(25)

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PARTIAL DIFFERENTIAL EQUATIONS AND ANALYTICAL CALCULUS

ABSTRACT

is very pedagogical thes questions and Partial differential equation, in mathematics, equation relating a function of several variables to its partial derivatives. A partial derivative of a function of several variables expresses how fast the function changes when one of its variables is changed, the others being held constant (compare ordinary differential equation). The partial derivative of a function is again a function, and, if f(x, y) denotes the original function of the variables x and y, the partial derivative with respect to x—i.e., when only x is allowed to vary—is typically written as fx(x, y) or ∂f/∂x. The operation of finding a partial derivative can be applied to a function that is itself a partial derivative of another function to get what is called a second-order partial derivative.In general, partial differential equations are difficult to solve, but techniques have been developed for simpler classes of equations called linear, and for classes known loosely as “almost” linear, in which all derivatives of an order higher than one occur to the first power and their coefficients involve only the independent variables.

Many physically important partial differential equations are second-order and linear. For example:

For an analogous treatment of elliptic curves defined as complete intersection in higher dimensional toric varieties, see the module weierstrass_higher.

Technically, this module computes the Weierstrass form of the Jacobian of the elliptic curve. This is why you will never have to specify the origin (or zero section) in the following and as established prof dr mircea orasanu these contribution appear a JACOBIAN and Louis University where work prof dr mircea orasanu but other can be not using some important equations

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in problem to approach we approach that are extended important considerations of algebraic structures as N is a monoid

Z is an integral domain

Q is a field

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the field C is algebraically complete observed prof dr mircea orasanu that have not find by dir dudian lyc 39 because that he not known that you have been asked by a child to give them arithmetic problems, so they could show off their newly learned skills in addition and subtraction I’m sure that after a few problems such as: 2 + 3, 9 – 5, 10 + 2 and 6 – 4, you tried tossing them something a little more difficult: 4 – 7 only to be told “ That’s not allowed.” thus appear the ring of modulo (n) natural integer with considerations established by prof dr mircea orasanu inspired by e. galois and may not have realized is that you and the child did not just have different objects in mind (negative numbers) but entirely different algebraic systems. In other words a set of objects (they could be natural numbers, integers or reals) and a set of operations, or rules regarding how the numbers can be combined. thus these aspects are all unknown in FAC MAT bucharest We will take a very informal tour of some algebraic systems, but before we define some of the terms, let us build a structure which will have some necessary properties for examples and counterexamples that will help us clarify some of the definitions.