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An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

Decimal is the base-10 notational system for representing real numbers. The expression of a number using the decimal system is called its decimal expansion, examples of which ...

The symbol used to separate the integer part of a decimal number from its fractional part is called the decimal point. In the United States, the decimal point is denoted with ...

Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...

The partial order width of a set P is equal to the minimum number of chains needed to cover P. Equivalently, if a set P of ab+1 elements is partially ordered, then P contains ...

Direct search factorization is the simplest (and most simple-minded) prime factorization algorithm. It consists of searching for factors of a number by systematically ...

Given an arithmetic progression of terms an+b, for n=1, 2, ..., the series contains an infinite number of primes if a and b are relatively prime, i.e., (a,b)=1. This result ...

A formula for the Bell polynomial and Bell numbers. The general formula states that B_n(x)=e^(-x)sum_(k=0)^infty(k^n)/(k!)x^k, (1) where B_n(x) is a Bell polynomial (Roman ...

For any alpha in A (where A denotes the set of algebraic numbers), let |alpha|^_ denote the maximum of moduli of all conjugates of alpha. Then a function ...

Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which ...