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When all the points P on one line are related by an isometry to all points P^' on another, the midpoints of the segments PP^' are either distinct and collinear or coincident.

If a prime number divides a norm but not the bases of the norm, it is itself a norm.

The Fermat number F_n is prime iff 3^(2^(2^n-1))=-1 (mod F_n).

A finite division algebra is a field.

The geometric centroid of a quadrilateral lamina is the center of its Wittenbauer's parallelogram.

Let the characteristic polynomial of an n×n complex matrix A be written in the form P(lambda) = |lambdaI-A| (1) = ...

A matching is a maximum matching iff it contains no augmenting path.

The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

If M^3 is a closed oriented connected 3-manifold such that every simple closed curve in M lies interior to a ball in M, then M is homeomorphic with the hypersphere, S^3.

If two complementary Plücker characteristics are equal, then each characteristic is equal to its complement except in four cases where the sum of order and class is 9.