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Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

Some computations allow shortcuts which can be used to speed them up. Consider the operation of raising a number to a positive integer power. It is possible, for example, to ...

The even part Ev(n) of a positive integer n is defined by Ev(n)=2^(b(n)), where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 2, ..., are 1, 2, ...

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...

The Mephisto waltz sequence is defined by beginning with 0 and then iterating the maps 0->001 and 1->110. This gives 0, 001, 001001110, 001001110001001110110110001, ... (OEIS ...

A magic square is said to be p-multimagic if the square formed by replacing each element by its kth power for k=1, 2, ..., p is also magic. A 2-multimagic square is called ...

The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient ...

By way of analogy with the eban numbers, oban numbers are defined as numbers whose English names do not contain the letter "o" (i.e., "o" is banned). Note that this ...