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Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

An operator of period 2, i.e., an operator * which satisfies ((a)^*)^*=a.

The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral ...

A polygonal number of the form n(5n-3)/2. The first few are 1, 7, 18, 34, 55, 81, 112, ... (OEIS A000566). The generating function for the heptagonal numbers is ...

A quantity which takes on the value zero is said to vanish. For example, the function f(z)=z^2 vanishes at the point z=0. For emphasis, the term "vanish identically" is ...

A coordinate system (mu,nu,psi) given by the coordinate transformation x = (mucospsi)/(mu^2+nu^2) (1) y = (musinpsi)/(mu^2+nu^2) (2) z = nu/(mu^2+nu^2) (3) and defined for ...

It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

A tetrahedron having a trihedron all of the face angles of which are right angles. The face opposite the vertex of the right angles is called the base. If the edge lengths ...

The identity (xy)x^2=x(yx^2) satisfied by elements x and y in a Jordan algebra.

A quantity that is nonzero everywhere is said to be nonvanishing. For instance, the values of x^2+1 are nonvanishing for real x, while those of x^2 are not (since x^2 ...