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Let (x_1,x_2) and (y_1,y_2,y_3) be two sets of complex numbers linearly independent over the rationals. Then at least one of ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n-1 ...

Every finite simple group (that is not cyclic) has even group order, and the group order of every finite simple noncommutative group is doubly even, i.e., divisible by 4 ...

A generalization of the Kronecker decomposition theorem which states that every finitely generated Abelian group is isomorphic to the group direct sum of a finite number of ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

The locus of the centers of all circumconics that also pass through the orthocenter of a triangle (which, when not degenerate, are rectangular hyperbolas) is a circle through ...

Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N=a (mod r) (1) and N=b (mod s). (2) ...

The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a ...