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The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

Given a group with elements A and X, there must be an element B which is a similarity transformation of A,B=X^(-1)AX so A and B are conjugate with respect to X. Conjugate ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

Characterized by allowing only integer values.

A domatic partition is a partition of the vertices of a graph into disjoint dominating sets. The maximum number of disjoint dominating sets in a domatic partition of a graph ...

An even perfect number is perfect number that is even, i.e., an even number n whose sum of divisors (including n itself) equals n. All known perfect numbers are even, and ...

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...

In a category C, an initial object is an object I in Ob(C) such that for any other object X in Ob(C), there is one and only one morphism from I to X.

Simple majority vote is the only procedure which is anonymous, dual, and monotonic.